On the Short Surface Fatigue Crack Growth Behavior in a Fine-Grained WC-Co Cemented Carbide

: In the present study, the fatigue crack growth (FCG) behavior of short surface cracks in a ﬁne-grained cemented carbide with a length of less than 1 mm was investigated. The rotating bending and the four-point bending fatigue tests were carried out at stress ratios of R = − 1 and R = 0.1 ( R = maximum stress/minimum stress). It was found that a short surface crack had a longer stable fatigue crack growth area than a long through-thickness crack; the FCG behaviors of the two types of crack are clearly different. Furthermore, the FCG path of short surface cracks was investigated in detail to study the interaction between fatigue cracks and microstructures of the cemented carbide such as WC grains and the Co phase. At a low K max ( K max = the maximum stress intensity factor), it was found that fatigue crack growth within WC grains is difﬁcult because of a small driving force; instead, crack growth is along the brittle WC/WC interface. On the other hand, at a high K max , WC grain breakage often occurs, since the driving force of FCG is large, and the fatigue crack grows linearly.


Introduction
Cemented carbides are widely used for cutting tools, dies, mechanical parts, and so forth [1], because of their superior abrasive wear resistance to tool steels. Among the cemented carbides, WC-Co alloys have superior mechanical properties and are highly versatile and widely used [2]. The mechanical properties of cemented carbides are intermediate between those of brittle materials, such as ceramics and cermets, and ductile materials such as tool steels. In general, the extent of the brittleness increases as the Co content decreases and the WC grain size decreases. More specifically, as the Co content increases, the toughness of the material increases, but the hardness decreases. As the WC grain size increases, the toughness of the material increases, but the hardness decreases [3].
There have recently been increasing cases of utilizing cemented carbides for metal dies and increasing demand for long-life dies. When a cemented carbide is applied to a metal die, it may become useless after long-term use due to the fatigue crack growth (FCG). It is desirable to use WC-Co dies safely for long durations without fracture failures such as chipping, cracking, or rupture. Therefore, it is extremely important to understand the relationship between the FCG behavior of cemented carbides and their microstructures such as WC grain and the Co phase [4].
Previous studies on the fatigue behavior of cemented carbides can be broadly classified into (1) determination of the fatigue lifetime and fatigue limit, and (2) evaluation of the FCG behavior based on fracture mechanics or damage tolerance mechanics.
There have been numerous studies in the former category. For example, many papers have reported that the fatigue strength of cemented carbide is decreased by applying a cyclic load [5]. In addition, the reduction of fatigue strength becomes marked with increasing Co content in the material [6][7][8][9][10][11]. In recent years, studies on the FCG behavior in the latter category have also been conducted, although many of them examined only the behavior of long through-thickness fatigue cracks.
Fry et al. [12] investigated the relationship between the rate of FCG, da/dN, and the stress intensity factor range, ∆K. They reported that the FCG resistance increases with increasing Co content, and with increasing WC grain size. Torres et al. [13] and Llanes et al. [14] studied the FCG behavior of long through-thickness cracks in cemented carbides. They clarified that the rate of FCG more strongly depends on the maximum stress intensity factor K max than the stress intensity factor range ∆K.
Boo et al. [15] investigated the FCG behavior of long through-thickness cracks in a cemented carbide. They reported that the Co phase at the crack tip undergoes a phase transformation from FCC to HCP when subjected to repeated loading, resulting in the embrittlement of the area and accelerated FCG. Sunouchi et al. [16] studied the FCG mechanism of long through-thickness cracks using the acoustic emission method. They showed that the lower FCG resistance of the cemented carbide at a high K max than that in steel and in aluminum alloys is due to transgranular cracking of WC grains. In addition, Mingard et al. [17] observed the FCG path of a long through-thickness fatigue crack in situ, using a scanning electron microscope (SEM) and a specially designed flat specimen [18].
The FCG behavior and the crack paths described above were for long through-thickness fatigue cracks. Excluding the following studies, there have been very few studies on the FCG behavior of short surface fatigue cracks, which often cause the surface cracking of dies made of cemented carbides.
Ishihara et al. [19] conducted four-point bending fatigue tests using rectangular specimens and investigated the FCG behavior of short surface fatigue cracks in a cemented carbide. They found that at a low K max , the cyclic stress loosens the interface between the WC grains and the binder phases, leading to the occurrence of microcracks at the interface in front of the crack tip. Repeated stress also eliminates bridging portions, located behind the crack tip.
When the crack driving force, K max , is sufficiently large to break WC grains, the crack growth process is mainly dominated by the transgranular cracking fracture of WC grains.
Ishihara et al. [20] also investigated the FCG behavior of short surface cracks in cermet, and found that its FCG behavior was similar to that of a cemented carbide. Mikado et al. [21] conducted a rotating bending fatigue test on a cemented carbide to evaluate its fatigue strength and the FCG behavior of short surface cracks in the material. It was found that reducing the rate of FCG at the initial stage of the fatigue fracture process is important for prolonging the fatigue lifetime.
As reviewed above, although the FCG behavior of long through-thickness cracks in cemented carbides has been studied, there has been limited research on the FCG behavior of short surface cracks and the crack growth pathway. This is because the observation of short surface fatigue cracks with a length on the order of 100 µm in hard brittle materials is extremely difficult compared with the observation of long through-thickness fatigue cracks. In addition, there has been no comparison of the difference between the FCG of short surface cracks and long through-thickness cracks.
In the present study, the FCG behavior of short surface cracks less than 1 mm in length in a cemented carbide were investigated for the first time. Then, a comparison was made between the FCG behavior of long through-thickness cracks and short surface cracks to clarify the difference between them. Furthermore, the crack growth pathway of short surface fatigue cracks was investigated in detail to study the interaction between fatigue cracks and the material microstructure, WC grains, and the Co phase.

Material
In the present study, a commercially available fine-grained WC-Co cemented carbide was used as the testing material. Tables 1 and 2 show the chemical composition and mechanical properties of the material, respectively. The material contains 13.0 wt % Co, and its bending strength is 4100 MPa. The Young's modulus was obtained from the catalog. The fracture toughness was the average value of five measurements by the single-edge-precracked-beam (SEPB) method [22]. The bending strength was the average value of three measurements by the three-point bending test using plane specimens as shown in the next section ( Figure 3a). The Vickers hardness was the average value of ten measurements performed with a Vickers hardness tester (FUTURE-TECH CORP., Kanagawa, Japan) under a load of 2.94 N and a holding time of 20 s. Figure 1 shows the microstructure of the material, which is a composite microstructure consisting of both a WC and a Co phase. Figure 2a,b shows histograms of the WC grain size and binder mean free path, respectively, constructed from the observation of the microstructure shown in Figure 1. The material has a log-normal distribution of WC grain size with a modal value of about 0.35 µm, and has an exponential distributed binder mean free path ranging from 0 to 1 µm. Table 1. Chemical composition of the WC-Co cemented carbide (wt %).

Co
Cr W and C 13.0 0.51 Bal.

Material
In the present study, a commercially available fine-grained WC-Co cemented carbide was used as the testing material. Tables 1 and 2 show the chemical composition and mechanical properties of the material, respectively. The material contains 13.0 wt % Co, and its bending strength is 4100 MPa. The Young's modulus was obtained from the catalog. The fracture toughness was the average value of five measurements by the single-edge-precracked-beam (SEPB) method [22]. The bending strength was the average value of three measurements by the three-point bending test using plane specimens as shown in the next section ( Figure 3a). The Vickers hardness was the average value of ten measurements performed with a Vickers hardness tester (FUTURE-TECH CORP., Kanagawa, Japan) under a load of 2.94 N and a holding time of 20 s. Figure 1 shows the microstructure of the material, which is a composite microstructure consisting of both a WC and a Co phase. Figure 2a,b shows histograms of the WC grain size and binder mean free path, respectively, constructed from the observation of the microstructure shown in Figure 1. The material has a log-normal distribution of WC grain size with a modal value of about 0.35 μm, and has an exponential distributed binder mean free path ranging from 0 to 1 μm. Table 1. Chemical composition of the WC-Co cemented carbide (wt %).

Co
Cr W and C 13.0 0.51 Bal.

Specimens
The shapes and dimensions of the specimens used in the present study are shown in Figure 3. Two types of hourglass-shaped specimens with a minimum diameter of 3 mm were used: the un-notched specimen shown in Figure 3a, and the notched specimen shown in Figure 3b. The former was used to investigate the S-N curve of the material at a stress ratio of R = −1, while the latter was used to study the FCG rate of short surface cracks in the material at R = −1. Specimens of both types were polished to a mirror-like finish with diamond paste (particle size of 1 μm) to minimize the effects of roughness and residual stress. The surface roughness Ra of the polished specimens was less than 0.1 μm. The compressive residual stress σr on the surface of the polished specimens was less than 500 MPa in the WC phase and less than 200 MPa in the Co phase. For the notched specimen, an artificial notch with a length of 0.08 mm, a width of 0.02 mm, and a depth of 0.04 mm was introduced into the specimen surface by laser beam machining. In addition, four-point bending fatigue tests were conducted at R = 0.1 using the rectangular specimens. Figure 4 shows the shape and dimensions of the specimen, which were 8 mm wide, 4 mm high, and 50 mm long. A Vickers indentation (indentation load: 400 N and indentation time 20 s.) was introduced on the center of the specimens to make a pre-crack.

Specimens
The shapes and dimensions of the specimens used in the present study are shown in Figure 3. Two types of hourglass-shaped specimens with a minimum diameter of 3 mm were used: the un-notched specimen shown in Figure 3a, and the notched specimen shown in Figure 3b. The former was used to investigate the S-N curve of the material at a stress ratio of R = −1, while the latter was used to study the FCG rate of short surface cracks in the material at R = −1. Specimens of both types were polished to a mirror-like finish with diamond paste (particle size of 1 µm) to minimize the effects of roughness and residual stress. The surface roughness R a of the polished specimens was less than 0.1 µm. The compressive residual stress σ r on the surface of the polished specimens was less than 500 MPa in the WC phase and less than 200 MPa in the Co phase. For the notched specimen, an artificial notch with a length of 0.08 mm, a width of 0.02 mm, and a depth of 0.04 mm was introduced into the specimen surface by laser beam machining. In addition, four-point bending fatigue tests were conducted at R = 0.1 using the rectangular specimens. Figure 4 shows the shape and dimensions of the specimen, which were 8 mm wide, 4 mm high, and 50 mm long. A Vickers indentation (indentation load: 400 N and indentation time 20 s.) was introduced on the center of the specimens to make a pre-crack.

Specimens
The shapes and dimensions of the specimens used in the present study are shown in Figure 3. Two types of hourglass-shaped specimens with a minimum diameter of 3 mm were used: the un-notched specimen shown in Figure 3a, and the notched specimen shown in Figure 3b. The former was used to investigate the S-N curve of the material at a stress ratio of R = −1, while the latter was used to study the FCG rate of short surface cracks in the material at R = −1. Specimens of both types were polished to a mirror-like finish with diamond paste (particle size of 1 μm) to minimize the effects of roughness and residual stress. The surface roughness Ra of the polished specimens was less than 0.1 μm. The compressive residual stress σr on the surface of the polished specimens was less than 500 MPa in the WC phase and less than 200 MPa in the Co phase. For the notched specimen, an artificial notch with a length of 0.08 mm, a width of 0.02 mm, and a depth of 0.04 mm was introduced into the specimen surface by laser beam machining. In addition, four-point bending fatigue tests were conducted at R = 0.1 using the rectangular specimens. Figure 4 shows the shape and dimensions of the specimen, which were 8 mm wide, 4 mm high, and 50 mm long. A Vickers indentation (indentation load: 400 N and indentation time 20 s.) was introduced on the center of the specimens to make a pre-crack.      Rotating bending fatigue tests were conducted in air at room temperature at a stress ratio of R = −1 with a stress frequency of 10-15 Hz. The un-notched and notched specimens shown in Figure 3a,b were respectively used to evaluate the fatigue lifetime and the rate of FCG for short surface cracks. The fatigue tests on the notched specimen were interrupted periodically to collect specimen-surface replicas. Acetylcellulose films and acetone were utilized for the replica films and the solvent, respectively. The lengths of fatigue cracks transcribed on these replica films were measured using a laser microscope. Two types of FCG test were conducted: FCG tests under constant stress amplitudes (increasing-Kmax tests), and FCG tests at a constant Kmax. The rate of FCG, da/dN, can be obtained from the plot of 2a versus N, where 2a and N are the crack length and the number of stress cycles, respectively. For the constant stress amplitude tests, the values of da/dN were determined as the slope of the approximate fitting curve to the experimental data at several measurement points. On the other hand, for the constant Kmax tests, the values of da/dN were determined as the slope of the approximate straight lines fitted to the experimental data at each Kmax value. Figure 5a shows the specimen surface after the laser beam machining. In this figure, discoloration due to the effect of laser heating can be seen around the notch. It was confirmed that there was some melting of the material as shown in Figure 5b and some cobalt oxidation as shown in Figure 5c in the discolored region. The heat-affected zone was determined as the discolored region. The total length of the discolored region is about 120 to 140 μm. Figure 5d shows the appearance of a short surface fatigue crack that was initiated and grew from an artificial notch. To eliminate the effect of the heat-affected zone, the region used to measure the rate of FCG was set outside the heat-affected zone.
On the driving force of fatigue cracks in brittle and microscopically heterogeneous materials, a common understanding has not yet been established. In the present study, the maximum stress intensity factor, Kmax, was utilized, as in previous studies [4,21]. To calculate the Kmax, the following expression was used: where σmax is the maximum stress, a is a half the crack length, and Y is the crack shape correction factor. A value of 0.73 was used for Y assuming that the crack is semicircular [23]. An actual crack does not grow along a straight path, but along a zigzag path because it usually grows along a WC/Co boundary as shown later. The crack length projected in the stress loading direction was employed as the crack length 2a in this study.
To investigate the crack growth path in detail, FCG tests were conducted at several constant values of Kmax using the notched specimen in Figure 3b. The stress amplitude σa was adjusted to an appropriate value to maintain a constant value of Kmax during the fatigue tests, since Kmax increases with the crack length under a constant stress amplitude. The crack growth path was observed on the specimen surface until the failure of the specimen. After the specimen failure, the fracture surface was also investigated in detail using an SEM to reveal the crack growth path on the fracture surface. Rotating bending fatigue tests were conducted in air at room temperature at a stress ratio of R = −1 with a stress frequency of 10-15 Hz. The un-notched and notched specimens shown in Figure 3a,b were respectively used to evaluate the fatigue lifetime and the rate of FCG for short surface cracks. The fatigue tests on the notched specimen were interrupted periodically to collect specimen-surface replicas. Acetylcellulose films and acetone were utilized for the replica films and the solvent, respectively. The lengths of fatigue cracks transcribed on these replica films were measured using a laser microscope. Two types of FCG test were conducted: FCG tests under constant stress amplitudes (increasing-K max tests), and FCG tests at a constant K max . The rate of FCG, da/dN, can be obtained from the plot of 2a versus N, where 2a and N are the crack length and the number of stress cycles, respectively. For the constant stress amplitude tests, the values of da/dN were determined as the slope of the approximate fitting curve to the experimental data at several measurement points. On the other hand, for the constant K max tests, the values of da/dN were determined as the slope of the approximate straight lines fitted to the experimental data at each K max value. Figure 5a shows the specimen surface after the laser beam machining. In this figure, discoloration due to the effect of laser heating can be seen around the notch. It was confirmed that there was some melting of the material as shown in Figure 5b and some cobalt oxidation as shown in Figure 5c in the discolored region. The heat-affected zone was determined as the discolored region. The total length of the discolored region is about 120 to 140 µm. Figure 5d shows the appearance of a short surface fatigue crack that was initiated and grew from an artificial notch. To eliminate the effect of the heat-affected zone, the region used to measure the rate of FCG was set outside the heat-affected zone.
On the driving force of fatigue cracks in brittle and microscopically heterogeneous materials, a common understanding has not yet been established. In the present study, the maximum stress intensity factor, K max , was utilized, as in previous studies [4,21]. To calculate the K max , the following expression was used: where σ max is the maximum stress, a is a half the crack length, and Y is the crack shape correction factor. A value of 0.73 was used for Y assuming that the crack is semicircular [23]. An actual crack does not grow along a straight path, but along a zigzag path because it usually grows along a WC/Co boundary as shown later. The crack length projected in the stress loading direction was employed as the crack length 2a in this study.
To investigate the crack growth path in detail, FCG tests were conducted at several constant values of K max using the notched specimen in Figure 3b. The stress amplitude σ a was adjusted to an appropriate value to maintain a constant value of K max during the fatigue tests, since K max increases with the crack length under a constant stress amplitude. The crack growth path was observed on the specimen surface until the failure of the specimen. After the specimen failure, the fracture surface was also investigated in detail using an SEM to reveal the crack growth path on the fracture surface. In addition to the rotating bending fatigue tests at the stress ratio R = −1, four-point bending fatigue tests (inner span: 10 mm, outer span: 30 mm) were also conducted at R = 0.1 using the rectangular specimens shown in Figure 4c. A Vickers indentation was introduced on the specimen surface to initiate a crack. To eliminate the effects of the indentation, such as those of machining and residual stress, on the FCG behavior of short surface cracks, the introduced crack was extended to a length of approximately 200 μm by applying a cyclic load. A servo-hydraulic fatigue testing machine was used to perform the four-point bending fatigue test. The tests were conducted in air at room temperature with a stress frequency of 10 Hz. The FCG behavior of short surface cracks was measured using the replication technique.

S-N Curve at R = −1
The S-N curve was investigated using the un-notched fatigue specimens. Figure 6 shows the S-N curve for the fine-grained WC-Co cemented carbide at a stress ratio of R = −1. The fatigue limit at R = −1 was estimated to be 1600 MPa. The solid line in the figure shows an approximate fitting curve to the experimental data. A fatigue test was conducted using one specimen for each stress amplitude, since a statistical analysis on the fatigue life is not the main purpose of this study. In addition to the rotating bending fatigue tests at the stress ratio R = −1, four-point bending fatigue tests (inner span: 10 mm, outer span: 30 mm) were also conducted at R = 0.1 using the rectangular specimens shown in Figure 4c. A Vickers indentation was introduced on the specimen surface to initiate a crack. To eliminate the effects of the indentation, such as those of machining and residual stress, on the FCG behavior of short surface cracks, the introduced crack was extended to a length of approximately 200 µm by applying a cyclic load. A servo-hydraulic fatigue testing machine was used to perform the four-point bending fatigue test. The tests were conducted in air at room temperature with a stress frequency of 10 Hz. The FCG behavior of short surface cracks was measured using the replication technique.

S-N Curve at R = −1
The S-N curve was investigated using the un-notched fatigue specimens. Figure 6 shows the S-N curve for the fine-grained WC-Co cemented carbide at a stress ratio of R = −1. The fatigue limit at R = −1 was estimated to be 1600 MPa. The solid line in the figure shows an approximate fitting curve to the experimental data. A fatigue test was conducted using one specimen for each stress amplitude, since a statistical analysis on the fatigue life is not the main purpose of this study.

Fatigue Crack Growth (FCG) Behavior of Short Surface Cracks
The FCG behavior of short surface cracks in the WC-Co cemented carbide was studied using the notched specimens. Figure 7 shows the variation of the crack length 2a as a function of the number of cycles N under several conditions at R = −1. Figure 7a shows the result under a constant stress amplitude σa of 600 MPa. Figure 7b,c shows the 2a vs. N relations for constant Kmax values of 6.0 and 7.5 MPam 1/2 , respectively. The rate of FCG, da/dN, under the constant-σa test was obtained from Figure 7a as the slope of the approximate fitting curve to the experimental data, and Kmax was calculated using Equation (1). The values of da/dN in the constant-Kmax tests in Figure 7b,c were similarly evaluated as the slopes of the approximate straight lines fitted to the experimental data. Figure 8a,b shows the relations between the rate of FCG, da/dN, and the Kmax obtained at stress ratios of R = −1 and 0.1, respectively. In these figures, the experimental results are plotted for the constant-σa tests (open circles) and the constant-Kmax tests (black and gray solid circles). Focusing on the effect of the stress ratio by comparing the results of Figure 8a, b, little difference due to the stress ratio can be seen in the da/dN vs. Kmax relations.

Fatigue Crack Growth (FCG) Behavior of Short Surface Cracks
The FCG behavior of short surface cracks in the WC-Co cemented carbide was studied using the notched specimens. Figure 7 shows the variation of the crack length 2a as a function of the number of cycles N under several conditions at R = −1. Figure 7a shows the result under a constant stress amplitude σ a of 600 MPa. Figure 7b,c shows the 2a vs. N relations for constant K max values of 6.0 and 7.5 MPam 1/2 , respectively. The rate of FCG, da/dN, under the constant-σ a test was obtained from Figure 7a as the slope of the approximate fitting curve to the experimental data, and K max was calculated using Equation (1). The values of da/dN in the constant-K max tests in Figure 7b,c were similarly evaluated as the slopes of the approximate straight lines fitted to the experimental data. Figure 8a,b shows the relations between the rate of FCG, da/dN, and the K max obtained at stress ratios of R = −1 and 0.1, respectively. In these figures, the experimental results are plotted for the constant-σ a tests (open circles) and the constant-K max tests (black and gray solid circles). Focusing on the effect of the stress ratio by comparing the results of Figure 8a, b, little difference due to the stress ratio can be seen in the da/dN vs. K max relations.

Fatigue Crack Growth (FCG) Behavior of Short Surface Cracks
The FCG behavior of short surface cracks in the WC-Co cemented carbide was studied using the notched specimens. Figure 7 shows the variation of the crack length 2a as a function of the number of cycles N under several conditions at R = −1. Figure 7a shows the result under a constant stress amplitude σa of 600 MPa. Figure 7b,c shows the 2a vs. N relations for constant Kmax values of 6.0 and 7.5 MPam 1/2 , respectively. The rate of FCG, da/dN, under the constant-σa test was obtained from Figure 7a as the slope of the approximate fitting curve to the experimental data, and Kmax was calculated using Equation (1). The values of da/dN in the constant-Kmax tests in Figure 7b,c were similarly evaluated as the slopes of the approximate straight lines fitted to the experimental data. Figure 8a,b shows the relations between the rate of FCG, da/dN, and the Kmax obtained at stress ratios of R = −1 and 0.1, respectively. In these figures, the experimental results are plotted for the constant-σa tests (open circles) and the constant-Kmax tests (black and gray solid circles). Focusing on the effect of the stress ratio by comparing the results of Figure 8a, b, little difference due to the stress ratio can be seen in the da/dN vs. Kmax relations.

Observation of the Crack Growth Path
The crack growth path was investigated in detail for R = −1 and under the constant-Kmax conditions (Figure 7b,c). Special attention was paid to the interaction between the fatigue crack and the microstructure (WC grains and the Co phase), particularly the effect of Kmax on the FCG path. The observations were conducted in two ways. First, after interrupting the FCG test, the specimen surface was investigated in detail using the SEM. Second, after the failure of a specimen, its fracture

Observation of the Crack Growth Path
The crack growth path was investigated in detail for R = −1 and under the constant-Kmax conditions (Figure 7b,c). Special attention was paid to the interaction between the fatigue crack and the microstructure (WC grains and the Co phase), particularly the effect of Kmax on the FCG path. The observations were conducted in two ways. First, after interrupting the FCG test, the specimen surface was investigated in detail using the SEM. Second, after the failure of a specimen, its fracture

Observation of the Crack Growth Path
The crack growth path was investigated in detail for R = −1 and under the constant-K max conditions (Figure 7b,c). Special attention was paid to the interaction between the fatigue crack and the microstructure (WC grains and the Co phase), particularly the effect of K max on the FCG path.
The observations were conducted in two ways. First, after interrupting the FCG test, the specimen surface was investigated in detail using the SEM. Second, after the failure of a specimen, its fracture surface was observed using the SEM. To clarify the relationship between the observations of the fracture surface and specimen surface, the same locations of the fatigue specimen were selected for the two observations. Figure 9 shows The observed crack growth paths on the specimen surfaces were classified into four types [17]: (1) within WC grains, (2) within the Co phase, (3) along the WC/WC boundaries, and (4) along the WC/Co boundaries. As can be seen from Figure 9a-A,a-B, at the low K max value of 6.0 MPam 1/2 , the crack mainly grew along the WC/WC boundaries (type (3)) among the above four types of crack growth paths. This finding can also be confirmed from the fracture surface in Figure 9a-C, where many missing portions of WC grains exist, as highlighted by the yellow arrows. This indicates that the crack grew along the WC/WC boundaries at the low value of K max . In contrast, at the higher K max value of 7.5 MPam 1/2 (Figure 9b-A,B), many cleavage fractures of WC grains were observed compared with at the low value of K max . This can also be confirmed from the fracture surfaces, where there are many cleavage faces, as highlighted by the yellow arrows in Figure 9b-C. Thus, the crack grew within WC grains more frequently at the higher value of K max . In the fatigue crack growth process of cemented carbides, WC grains form bridging, which is usually formed behind the main crack tip. As indicated by the black arrow in Figure 9b-B, for example, the existence of bridging can be confirmed. It appears that there is another crack in addition to the main crack. Figure 9 shows part of a crack growth path in detail. The observed crack growth paths on specimen surfaces with a large area were classified into four types, and the percentages of each type of crack growth path were evaluated at several K max values. The results of the classification are shown in Figure 10, in which the percentages of the four types of crack growth path are shown as a function of K max . The percentage of type (3) paths, i.e., along the WC/WC boundaries, decreased from 50 to 30% with an increase in K max from 6.0 to 7.5 MPam 1/2 , whereas the percentage of type (1) paths, i.e., within WC grains, increased from 20 to 40%. surface was observed using the SEM. To clarify the relationship between the observations of the fracture surface and specimen surface, the same locations of the fatigue specimen were selected for the two observations. Figure 9 shows The observed crack growth paths on the specimen surfaces were classified into four types [17]: (1) within WC grains, (2) within the Co phase, (3) along the WC/WC boundaries, and (4) along the WC/Co boundaries. As can be seen from Figure 9a-A,a-B, at the low Kmax value of 6.0 MPam 1/2 , the crack mainly grew along the WC/WC boundaries (type (3)) among the above four types of crack growth paths. This finding can also be confirmed from the fracture surface in Figure 9a-C, where many missing portions of WC grains exist, as highlighted by the yellow arrows. This indicates that the crack grew along the WC/WC boundaries at the low value of Kmax. In contrast, at the higher Kmax value of 7.5 MPam 1/2 (Figure 9b-A,B), many cleavage fractures of WC grains were observed compared with at the low value of Kmax. This can also be confirmed from the fracture surfaces, where there are many cleavage faces, as highlighted by the yellow arrows in Figure 9b-C. Thus, the crack grew within WC grains more frequently at the higher value of Kmax. In the fatigue crack growth process of cemented carbides, WC grains form bridging, which is usually formed behind the main crack tip. As indicated by the black arrow in Figure 9b-B, for example, the existence of bridging can be confirmed. It appears that there is another crack in addition to the main crack. Figure 9 shows part of a crack growth path in detail. The observed crack growth paths on specimen surfaces with a large area were classified into four types, and the percentages of each type of crack growth path were evaluated at several Kmax values. The results of the classification are shown in Figure 10, in which the percentages of the four types of crack growth path are shown as a function of Kmax. The percentage of type (3) paths, i.e., along the WC/WC boundaries, decreased from 50 to 30% with an increase in Kmax from 6.0 to 7.5 MPam 1/2 , whereas the percentage of type (1) paths, i.e., within WC grains, increased from 20 to 40%.

Crack growth
within WC grain WC/WC boundary WC/Co boundary within Co phase     Figure 11a shows the fracture surface at the low Kmax near the crack origin, and Figure  11b shows the fracture surface at the high Kmax far from the crack origin. The Kmax values for surface cracks with a half crack length a, were calculated using the following expression, where the crack length was measured from the crack origin:      Figure 11a shows the fracture surface at the low Kmax near the crack origin, and Figure  11b shows the fracture surface at the high Kmax far from the crack origin. The Kmax values for surface cracks with a half crack length a, were calculated using the following expression, where the crack length was measured from the crack origin: Figure 10. Relationship between percentage of each type of crack growth path and K max , observed at R = −1. Figure 11 shows SEM images of the fracture surface of an un-notched specimen that failed at σ a of 1600 MPa. Figure 11a shows the fracture surface at the low K max near the crack origin, and Figure 11b shows the fracture surface at the high K max far from the crack origin. The K max values for surface cracks with a half crack length a, were calculated using the following expression, where the crack length was measured from the crack origin: In this calculation, an internal crack slightly beneath the specimen surface was regarded as a surface crack with a semicircular shape. Therefore, a value of 0.73 was used for Y, as used in Equation (1). From the fracture surface observations, it was confirmed that the fatigue crack initiation site for the present material was an aggregate of several WC grains or a coarse WC grain slightly beneath the specimen surface [21].
There is a noticeable difference between the two images in Figure 11. On the fracture surface near the fracture origin in Figure 11a (at the low K max ), some missing portions of WC grains were also observed, as highlighted by the red arrows at the low K max . In contrast, on the fracture surface far from the fracture origin shown in Figure 11b (at the high K max ), several cleavage fractures of the WC grains were observed, as highlighted by the blue arrows. The above observations of the fracture surfaces were in good agreement with the results shown in Figure 10. (2) In this calculation, an internal crack slightly beneath the specimen surface was regarded as a surface crack with a semicircular shape. Therefore, a value of 0.73 was used for Y, as used in equation 1. From the fracture surface observations, it was confirmed that the fatigue crack initiation site for the present material was an aggregate of several WC grains or a coarse WC grain slightly beneath the specimen surface [21].
There is a noticeable difference between the two images in Figure 11. On the fracture surface near the fracture origin in Figure 11a (at the low Kmax), some missing portions of WC grains were also observed, as highlighted by the red arrows at the low Kmax. In contrast, on the fracture surface far from the fracture origin shown in Figure 11b (at the high Kmax), several cleavage fractures of the WC grains were observed, as highlighted by the blue arrows. The above observations of the fracture surfaces were in good agreement with the results shown in Figure 10.  Figure 12 shows the variation of the rate of FCG, da/dN, for a short surface crack as a function of the microstructure observed along the FCG path. FCG tests were interrupted periodically to observe the crack. Then, the specimen was removed from the fatigue testing machine and placed in an SEM. The crack length was measured while the specimen was in the SEM. da/dN was measured in several zones, indicated as (1)(2)(3)(4)(5) in the figure. da/dN in zone (3) (the cleavage fracture zone of WC grains)  Figure 12 shows the variation of the rate of FCG, da/dN, for a short surface crack as a function of the microstructure observed along the FCG path. FCG tests were interrupted periodically to observe the crack. Then, the specimen was removed from the fatigue testing machine and placed in an SEM. The crack length was measured while the specimen was in the SEM. da/dN was measured in several zones, indicated as (1)(2)(3)(4)(5) in the figure. da/dN in zone (3) (the cleavage fracture zone of WC grains) was higher than that in the other zones, indicating that the FCG resistance was lowest within WC grains. Crack tortuosity and bridging parts can be seen in zone (4), i.e., at the WC/WC or WC/Co boundaries. da/dN in this zone was much lower than in the other zones.

Effect of the Microstructure on the Rate of FCG
was higher than that in the other zones, indicating that the FCG resistance was lowest within WC grains. Crack tortuosity and bridging parts can be seen in zone (4), i.e., at the WC/WC or WC/Co boundaries. da/dN in this zone was much lower than in the other zones.

Difference in the FCG Behavior Between Short Surface Cracks and Long Through-Thickness Cracks
The FCG behavior of short surface cracks obtained in the present study was expected to be different from that of long through-thickness cracks. In the following, the FCG behavior of long through-thickness cracks [4] previously obtained using the same cemented carbide will be compared with that of short surface cracks. FCG tests on the long through-thickness cracks were conducted at a stress ratio of R = 0.1 and at a stress frequency of 10 Hz using CT (Compact Tension) specimens [4]. The result is shown in Figure 13. In this figure, the FCG data for long through-thickness cracks (stress ratio R = 0.1) obtained by other researchers [14] using a similar fine-grained cemented carbide to that used in the present study are also shown. The FCG data can be approximated by straight lines on the logarithmic graph, and the following Paris equations [24] were derived: The power exponent m in the above equation was approximately 2 for short surface fatigue cracks but about 10 for long through-thickness fatigue cracks.
It is well known that residual stress on a specimen's surface strongly affects the crack growth behavior, even at small scales such as on thin films. For example, Ghidelli et al. [25] evaluated the elastic moduli on thin films considering the effect of residual stress. However, when the residual stress varies with time, as in fatigue crack growth, evaluation of the effects of residual stress often involves complicated stress analysis. Therefore, there have been very few studies on the FCG of cemented carbides considering the effects of residual stress. Thus, in this study, to study the FCG behavior, the specimen surface was polished to a mirror-like finish to minimize the effects of compressive residual stress induced by machining. The obtained data was compared with that of

Difference in the FCG Behavior Between Short Surface Cracks and Long Through-Thickness Cracks
The FCG behavior of short surface cracks obtained in the present study was expected to be different from that of long through-thickness cracks. In the following, the FCG behavior of long through-thickness cracks [4] previously obtained using the same cemented carbide will be compared with that of short surface cracks. FCG tests on the long through-thickness cracks were conducted at a stress ratio of R = 0.1 and at a stress frequency of 10 Hz using CT (Compact Tension) specimens [4]. The result is shown in Figure 13. In this figure, the FCG data for long through-thickness cracks (stress ratio R = 0.1) obtained by other researchers [14] using a similar fine-grained cemented carbide to that used in the present study are also shown. The FCG data can be approximated by straight lines on the logarithmic graph, and the following Paris equations [24] were derived: The power exponent m in the above equation was approximately 2 for short surface fatigue cracks but about 10 for long through-thickness fatigue cracks.
It is well known that residual stress on a specimen's surface strongly affects the crack growth behavior, even at small scales such as on thin films. For example, Ghidelli et al. [25] evaluated the elastic moduli on thin films considering the effect of residual stress. However, when the residual stress varies with time, as in fatigue crack growth, evaluation of the effects of residual stress often involves complicated stress analysis. Therefore, there have been very few studies on the FCG of cemented carbides considering the effects of residual stress. Thus, in this study, to study the FCG behavior, the specimen surface was polished to a mirror-like finish to minimize the effects of compressive residual stress induced by machining. The obtained data was compared with that of other researchers, where the effects of residual stress were not taken into consideration, in contrast to in our study. This is the main reason for not considering the effects of residual stress on FCG in this study. More detailed research on the effect of residual stress on the FCG behavior of cemented carbide will be carried out in the future.
As can be seen from the figure, the short surface fatigue crack has a longer region where the fatigue crack grows stably than the long through-thickness fatigue crack. Thus, the FCG behaviors of short surface and long through-thickness fatigue cracks are clearly different.
The K max value (hereinafter referred to as K fc ), at which the crack begins to grow unstably (da/dN > 10 −6 m/cycles) was determined to be 10 MPam 1/2 for the short surface fatigue crack, compared with 7.5 MPam 1/2 for the long through-thickness fatigue crack. It was found that the long through-thickness crack grows in a more brittle and unstable manner than the short surface fatigue crack.
In Figure 13, the K max value at the fatigue crack growth rate da/dN of 10 −6 m/cycles is defined as K fc and that at a da/dN of 10 −9 m/cycles is defined as K th . Figure 14 shows the change in the ratio of K th /K fc as a function of the average thickness of the Co phase, λ Co . In this figure, the experimental results obtained by Fry et al. [12] and by Llanes et al. [14] are also plotted. In their studies, similar cemented carbides to that in the present study were used. Table 3 shows the WC grain sizes and Co contents of the cemented carbides whose FCG data were plotted in Figure 14.
As shown in Figure 14, the tendency of fatigue susceptibility (K th /K fc ) in the crack growth behavior is not greatly affected by the difference in the WC-Co components of the materials. In other words, the difference between a long through-thickness crack and a short surface crack can be clearly seen even if the WC-Co components of the materials are different. The values of K th /K fc for long through-thickness fatigue cracks at R = 0.1 (black solid marks) were clearly larger than those of short surface fatigue cracks at R = −1 and 0.1 (open or gray circles). A clear difference was observed between the both types of crack. It is pointed out [14] that the mode of static fracture increases as the value of K th /K fc increases, and the fatigue behavior is strengthened as the value of K th /K fc decreases. Therefore, the results in Figures 13 and 14 show that the FCG behavior of short surface cracks is more susceptible to repeated stress than that of long through-thickness cracks.
other researchers, where the effects of residual stress were not taken into consideration, in contrast to in our study. This is the main reason for not considering the effects of residual stress on FCG in this study. More detailed research on the effect of residual stress on the FCG behavior of cemented carbide will be carried out in the future.
As can be seen from the figure, the short surface fatigue crack has a longer region where the fatigue crack grows stably than the long through-thickness fatigue crack. Thus, the FCG behaviors of short surface and long through-thickness fatigue cracks are clearly different.
The Kmax value (hereinafter referred to as Kfc), at which the crack begins to grow unstably (da/dN > 10 −6 m/cycles) was determined to be 10 MPam 1/2 for the short surface fatigue crack, compared with 7.5 MPam 1/2 for the long through-thickness fatigue crack. It was found that the long through-thickness crack grows in a more brittle and unstable manner than the short surface fatigue crack.
In Figure 13, the Kmax value at the fatigue crack growth rate da/dN of 10 −6 m/cycles is defined as Kfc and that at a da/dN of 10 −9 m/cycles is defined as Kth. Figure 14 shows the change in the ratio of Kth/Kfc as a function of the average thickness of the Co phase, λCo. In this figure, the experimental results obtained by Fry et al. [12] and by Llanes et al. [14] are also plotted. In their studies, similar cemented carbides to that in the present study were used. Table 3 shows the WC grain sizes and Co contents of the cemented carbides whose FCG data were plotted in Figure 14.
As shown in Figure 14, the tendency of fatigue susceptibility (Kth/Kfc) in the crack growth behavior is not greatly affected by the difference in the WC-Co components of the materials. In other words, the difference between a long through-thickness crack and a short surface crack can be clearly seen even if the WC-Co components of the materials are different. The values of Kth/Kfc for long through-thickness fatigue cracks at R = 0.1 (black solid marks) were clearly larger than those of short surface fatigue cracks at R = −1 and 0.1 (open or gray circles). A clear difference was observed between the both types of crack. It is pointed out [14] that the mode of static fracture increases as the value of Kth/Kfc increases, and the fatigue behavior is strengthened as the value of Kth/Kfc decreases. Therefore, the results in Figures 13 and 14 show that the FCG behavior of short surface cracks is more susceptible to repeated stress than that of long through-thickness cracks.   In the case of short surface fatigue cracks, the crack size is closer to the microstructure size of the material than for long through-thickness fatigue cracks. Thus, it is suspected that their FCG property is affected by the microstructure. As can be seen from Figure 9, the short surface fatigue cracks grow along the WC/WC grain interface in a zigzag manner while bypassing WC grains. Furthermore, as shown in zone (4) of Figure 12, a bridging effect is expected to occur, in which unbroken hard particles connect the upper and lower faces of the crack. Therefore, the above zigzag growth and bridging effect are more likely produced in the case of short surface fatigue cracks than in the case of long through-thickness fatigue cracks, which are followed by a decrease in the FCG driving force at the crack tip. As a result, it can be inferred that short surface fatigue cracks will grow more stably than long through-thickness fatigue cracks.
In a metal, it is well known that a short surface fatigue crack has a higher FCG rate than a long through-thickness fatigue crack at a low stress intensity factor range ΔK. A short surface fatigue crack will also grow under the threshold level of the stress intensity factor range ΔKth for a long through-thickness fatigue crack. In the present study, FCG data on the cemented carbide have not been systematically obtained in the low fatigue crack growth rate range, thus the difference between the FCG behavior of short surface cracks and long through-thickness cracks at the low values of Kmax has not yet been clarified. Further study on this issue is required.

Effect of the Maximum Stress Intensity Factor, Kmax, on the Crack Growth Path
To consider the effect of Kmax on the crack growth path, the size of the plastic zone rp at the crack tip was calculated using 2 max p y 1 2π Figure 14.
Fatigue sensitivity and microstructure relationship for fine-grained WC-Co cemented carbides. Table 3.
Microstructural properties and fatigue-testing conditions for several fine-grained cemented carbides.  In the case of short surface fatigue cracks, the crack size is closer to the microstructure size of the material than for long through-thickness fatigue cracks. Thus, it is suspected that their FCG property is affected by the microstructure. As can be seen from Figure 9, the short surface fatigue cracks grow along the WC/WC grain interface in a zigzag manner while bypassing WC grains. Furthermore, as shown in zone (4) of Figure 12, a bridging effect is expected to occur, in which unbroken hard particles connect the upper and lower faces of the crack. Therefore, the above zigzag growth and bridging effect are more likely produced in the case of short surface fatigue cracks than in the case of long through-thickness fatigue cracks, which are followed by a decrease in the FCG driving force at the crack tip. As a result, it can be inferred that short surface fatigue cracks will grow more stably than long through-thickness fatigue cracks.
In a metal, it is well known that a short surface fatigue crack has a higher FCG rate than a long through-thickness fatigue crack at a low stress intensity factor range ΔK. A short surface fatigue crack will also grow under the threshold level of the stress intensity factor range ΔKth for a long through-thickness fatigue crack. In the present study, FCG data on the cemented carbide have not been systematically obtained in the low fatigue crack growth rate range, thus the difference between the FCG behavior of short surface cracks and long through-thickness cracks at the low values of Kmax has not yet been clarified. Further study on this issue is required.

Effect of the Maximum Stress Intensity Factor, Kmax, on the Crack Growth Path
To consider the effect of Kmax on the crack growth path, the size of the plastic zone rp at the crack tip was calculated using 2 max p y 1 2π  Figure 14 Fatigue sensitivity and microstructure relationship for fine-grained WC-Co cemented carbides. Table 3. Microstructural properties and fatigue-testing conditions for several fine-grained cemented carbides.

Symbols Shown
in Figure 14 Co% (wt %) In the case of short surface fatigue cracks, the crack size is closer to the microstructure size of the material than for long through-thickness fatigue cracks. Thus, it is suspected that their FCG property is affected by the microstructure. As can be seen from Figure 9, the short surface fatigue cracks grow along the WC/WC grain interface in a zigzag manner while bypassing WC grains. Furthermore, as shown in zone (4) of Figure 12, a bridging effect is expected to occur, in which unbroken hard particles connect the upper and lower faces of the crack. Therefore, the above zigzag growth and bridging effect are more likely produced in the case of short surface fatigue cracks than in the case of long through-thickness fatigue cracks, which are followed by a decrease in the FCG driving force at the crack tip. As a result, it can be inferred that short surface fatigue cracks will grow more stably than long through-thickness fatigue cracks.
In a metal, it is well known that a short surface fatigue crack has a higher FCG rate than a long through-thickness fatigue crack at a low stress intensity factor range ΔK. A short surface fatigue crack will also grow under the threshold level of the stress intensity factor range ΔKth for a long through-thickness fatigue crack. In the present study, FCG data on the cemented carbide have not been systematically obtained in the low fatigue crack growth rate range, thus the difference between the FCG behavior of short surface cracks and long through-thickness cracks at the low values of Kmax has not yet been clarified. Further study on this issue is required.

Effect of the Maximum Stress Intensity Factor, Kmax, on the Crack Growth Path
To consider the effect of Kmax on the crack growth path, the size of the plastic zone rp at the crack tip was calculated using 2 max p y 1 2π  Figure 14 Fatigue sensitivity and microstructure relationship for fine-grained WC-Co cemented carbides. Table 3. Microstructural properties and fatigue-testing conditions for several fine-grained cemented carbides.

Symbols Shown
in Figure 14 Co% (wt %) In the case of short surface fatigue cracks, the crack size is closer to the microstructure size of the material than for long through-thickness fatigue cracks. Thus, it is suspected that their FCG property is affected by the microstructure. As can be seen from Figure 9, the short surface fatigue cracks grow along the WC/WC grain interface in a zigzag manner while bypassing WC grains. Furthermore, as shown in zone (4) of Figure 12, a bridging effect is expected to occur, in which unbroken hard particles connect the upper and lower faces of the crack. Therefore, the above zigzag growth and bridging effect are more likely produced in the case of short surface fatigue cracks than in the case of long through-thickness fatigue cracks, which are followed by a decrease in the FCG driving force at the crack tip. As a result, it can be inferred that short surface fatigue cracks will grow more stably than long through-thickness fatigue cracks.
In a metal, it is well known that a short surface fatigue crack has a higher FCG rate than a long through-thickness fatigue crack at a low stress intensity factor range ΔK. A short surface fatigue crack will also grow under the threshold level of the stress intensity factor range ΔKth for a long through-thickness fatigue crack. In the present study, FCG data on the cemented carbide have not been systematically obtained in the low fatigue crack growth rate range, thus the difference between the FCG behavior of short surface cracks and long through-thickness cracks at the low values of Kmax has not yet been clarified. Further study on this issue is required.

Effect of the Maximum Stress Intensity Factor, Kmax, on the Crack Growth Path
To consider the effect of Kmax on the crack growth path, the size of the plastic zone rp at the crack tip was calculated using 2 max p y 1 2π In the case of short surface fatigue cracks, the crack size is closer to the microstructure size of the material than for long through-thickness fatigue cracks. Thus, it is suspected that their FCG property is affected by the microstructure. As can be seen from Figure 9, the short surface fatigue cracks grow along the WC/WC grain interface in a zigzag manner while bypassing WC grains. Furthermore, as shown in zone (4) of Figure 12, a bridging effect is expected to occur, in which unbroken hard particles connect the upper and lower faces of the crack. Therefore, the above zigzag growth and bridging effect are more likely produced in the case of short surface fatigue cracks than in the case of long through-thickness fatigue cracks, which are followed by a decrease in the FCG driving force at the crack tip. As a result, it can be inferred that short surface fatigue cracks will grow more stably than long through-thickness fatigue cracks.
In a metal, it is well known that a short surface fatigue crack has a higher FCG rate than a long through-thickness fatigue crack at a low stress intensity factor range ΔK. A short surface fatigue crack will also grow under the threshold level of the stress intensity factor range ΔKth for a long through-thickness fatigue crack. In the present study, FCG data on the cemented carbide have not been systematically obtained in the low fatigue crack growth rate range, thus the difference between the FCG behavior of short surface cracks and long through-thickness cracks at the low values of Kmax has not yet been clarified. Further study on this issue is required.

Effect of the Maximum Stress Intensity Factor, Kmax, on the Crack Growth Path
To consider the effect of Kmax on the crack growth path, the size of the plastic zone rp at the crack tip was calculated using 2 max p y 1 2π In the case of short surface fatigue cracks, the crack size is closer to the microstructure size of the material than for long through-thickness fatigue cracks. Thus, it is suspected that their FCG property is affected by the microstructure. As can be seen from Figure 9, the short surface fatigue cracks grow along the WC/WC grain interface in a zigzag manner while bypassing WC grains. Furthermore, as shown in zone (4) of Figure 12, a bridging effect is expected to occur, in which unbroken hard particles connect the upper and lower faces of the crack. Therefore, the above zigzag growth and bridging effect are more likely produced in the case of short surface fatigue cracks than in the case of long through-thickness fatigue cracks, which are followed by a decrease in the FCG driving force at the crack tip. As a result, it can be inferred that short surface fatigue cracks will grow more stably than long through-thickness fatigue cracks.
In a metal, it is well known that a short surface fatigue crack has a higher FCG rate than a long through-thickness fatigue crack at a low stress intensity factor range ΔK. A short surface fatigue crack will also grow under the threshold level of the stress intensity factor range ΔKth for a long through-thickness fatigue crack. In the present study, FCG data on the cemented carbide have not been systematically obtained in the low fatigue crack growth rate range, thus the difference between the FCG behavior of short surface cracks and long through-thickness cracks at the low values of Kmax has not yet been clarified. Further study on this issue is required.

Effect of the Maximum Stress Intensity Factor, Kmax, on the Crack Growth Path
To consider the effect of Kmax on the crack growth path, the size of the plastic zone rp at the crack tip was calculated using 2 max p y 1 2π  In the case of short surface fatigue cracks, the crack size is closer to the microstructure size of the material than for long through-thickness fatigue cracks. Thus, it is suspected that their FCG property is affected by the microstructure. As can be seen from Figure 9, the short surface fatigue cracks grow along the WC/WC grain interface in a zigzag manner while bypassing WC grains. Furthermore, as shown in zone (4) of Figure 12, a bridging effect is expected to occur, in which unbroken hard particles connect the upper and lower faces of the crack. Therefore, the above zigzag growth and bridging effect are more likely produced in the case of short surface fatigue cracks than in the case of long through-thickness fatigue cracks, which are followed by a decrease in the FCG driving force at the crack tip. As a result, it can be inferred that short surface fatigue cracks will grow more stably than long through-thickness fatigue cracks.
In a metal, it is well known that a short surface fatigue crack has a higher FCG rate than a long through-thickness fatigue crack at a low stress intensity factor range ΔK. A short surface fatigue crack will also grow under the threshold level of the stress intensity factor range ΔKth for a long through-thickness fatigue crack. In the present study, FCG data on the cemented carbide have not been systematically obtained in the low fatigue crack growth rate range, thus the difference between the FCG behavior of short surface cracks and long through-thickness cracks at the low values of Kmax has not yet been clarified. Further study on this issue is required.

Effect of the Maximum Stress Intensity Factor, Kmax, on the Crack Growth Path
To consider the effect of Kmax on the crack growth path, the size of the plastic zone rp at the crack tip was calculated using 2 max p y 1 2π  In the case of short surface fatigue cracks, the crack size is closer to the microstructure size of the material than for long through-thickness fatigue cracks. Thus, it is suspected that their FCG property is affected by the microstructure. As can be seen from Figure 9, the short surface fatigue cracks grow along the WC/WC grain interface in a zigzag manner while bypassing WC grains. Furthermore, as shown in zone (4) of Figure 12, a bridging effect is expected to occur, in which unbroken hard particles connect the upper and lower faces of the crack. Therefore, the above zigzag growth and bridging effect are more likely produced in the case of short surface fatigue cracks than in the case of long through-thickness fatigue cracks, which are followed by a decrease in the FCG driving force at the crack tip. As a result, it can be inferred that short surface fatigue cracks will grow more stably than long through-thickness fatigue cracks.
In a metal, it is well known that a short surface fatigue crack has a higher FCG rate than a long through-thickness fatigue crack at a low stress intensity factor range ΔK. A short surface fatigue crack will also grow under the threshold level of the stress intensity factor range ΔKth for a long through-thickness fatigue crack. In the present study, FCG data on the cemented carbide have not been systematically obtained in the low fatigue crack growth rate range, thus the difference between the FCG behavior of short surface cracks and long through-thickness cracks at the low values of Kmax has not yet been clarified. Further study on this issue is required.

Effect of the Maximum Stress Intensity Factor, Kmax, on the Crack Growth Path
To consider the effect of Kmax on the crack growth path, the size of the plastic zone rp at the crack tip was calculated using 2 max p y 1 2π  In the case of short surface fatigue cracks, the crack size is closer to the microstructure size of the material than for long through-thickness fatigue cracks. Thus, it is suspected that their FCG property is affected by the microstructure. As can be seen from Figure 9, the short surface fatigue cracks grow along the WC/WC grain interface in a zigzag manner while bypassing WC grains. Furthermore, as shown in zone (4) of Figure 12, a bridging effect is expected to occur, in which unbroken hard particles connect the upper and lower faces of the crack. Therefore, the above zigzag growth and bridging effect are more likely produced in the case of short surface fatigue cracks than in the case of long through-thickness fatigue cracks, which are followed by a decrease in the FCG driving force at the crack tip. As a result, it can be inferred that short surface fatigue cracks will grow more stably than long through-thickness fatigue cracks.
In a metal, it is well known that a short surface fatigue crack has a higher FCG rate than a long through-thickness fatigue crack at a low stress intensity factor range ΔK. A short surface fatigue crack will also grow under the threshold level of the stress intensity factor range ΔKth for a long through-thickness fatigue crack. In the present study, FCG data on the cemented carbide have not been systematically obtained in the low fatigue crack growth rate range, thus the difference between the FCG behavior of short surface cracks and long through-thickness cracks at the low values of Kmax has not yet been clarified. Further study on this issue is required.

Effect of the Maximum Stress Intensity Factor, Kmax, on the Crack Growth Path
To consider the effect of Kmax on the crack growth path, the size of the plastic zone rp at the crack tip was calculated using 2 max p y 1 2π In the case of short surface fatigue cracks, the crack size is closer to the microstructure size of the material than for long through-thickness fatigue cracks. Thus, it is suspected that their FCG property is affected by the microstructure. As can be seen from Figure 9, the short surface fatigue cracks grow along the WC/WC grain interface in a zigzag manner while bypassing WC grains. Furthermore, as shown in zone (4) of Figure 12, a bridging effect is expected to occur, in which unbroken hard particles connect the upper and lower faces of the crack. Therefore, the above zigzag growth and bridging effect are more likely produced in the case of short surface fatigue cracks than in the case of long through-thickness fatigue cracks, which are followed by a decrease in the FCG driving force at the crack tip. As a result, it can be inferred that short surface fatigue cracks will grow more stably than long through-thickness fatigue cracks.
In a metal, it is well known that a short surface fatigue crack has a higher FCG rate than a long through-thickness fatigue crack at a low stress intensity factor range ∆K. A short surface fatigue crack will also grow under the threshold level of the stress intensity factor range ∆K th for a long through-thickness fatigue crack. In the present study, FCG data on the cemented carbide have not been systematically obtained in the low fatigue crack growth rate range, thus the difference between the FCG behavior of short surface cracks and long through-thickness cracks at the low values of K max has not yet been clarified. Further study on this issue is required.

Effect of the Maximum Stress Intensity Factor, K max , on the Crack Growth Path
To consider the effect of K max on the crack growth path, the size of the plastic zone r p at the crack tip was calculated using where σ y is the yield strength of the material, which is unknown at present. Thus, the bending strength indicated in Table 2 was used instead of the yield strength. The calculated values of r p for each value of K max are shown in Table 4. The calculation of the plastic zone size at the crack tip used in this paper is applicable only to a single-phase material. However, this calculation method was applied to easily obtain the plastic zone size at the crack tip in the material. Similar results were also obtained in the two-dimensional FEM (Finite Element Method) analysis reflecting the actual microstructure of the cemented carbide. The size of the plastic zone r p at the crack tip increases with K max as expected. At the low K max of 6.0 MPam 1/2 , r p of 0.34 µm is smaller than the average WC grain size (0.45 µm) of the present alloy. In this case, it is difficult for a crack to grow within WC grains, i.e., for transgranular cracking to occur. Instead, the crack is expected to grow preferentially along the weak WC/WC interfaces. On the other hand, at the high K max of 7.5 MPam 1/2 , r p of 0.53 µm is larger than the average WC grain size. In this case, the crack grows within WC grains and tends to be straighter than that for a low value of K max . It grows more rapidly because of the higher crack driving force and the fewer bridging parts than for the low value of K max . This mechanism is schematically illustrated in Figure 15.
where σy is the yield strength of the material, which is unknown at present. Thus, the bending strength indicated in Table 2 was used instead of the yield strength. The calculated values of rp for each value of Kmax are shown in Table 4. The calculation of the plastic zone size at the crack tip used in this paper is applicable only to a single-phase material. However, this calculation method was applied to easily obtain the plastic zone size at the crack tip in the material. Similar results were also obtained in the two-dimensional FEM (Finite Element Method) analysis reflecting the actual microstructure of the cemented carbide. The size of the plastic zone rp at the crack tip increases with Kmax as expected. At the low Kmax of 6.0 MPam 1/2 , rp of 0.34 μm is smaller than the average WC grain size (0.45 μm) of the present alloy. In this case, it is difficult for a crack to grow within WC grains, i.e., for transgranular cracking to occur. Instead, the crack is expected to grow preferentially along the weak WC/WC interfaces. On the other hand, at the high Kmax of 7.5 MPam 1/2 , rp of 0.53 μm is larger than the average WC grain size. In this case, the crack grows within WC grains and tends to be straighter than that for a low value of Kmax. It grows more rapidly because of the higher crack driving force and the fewer bridging parts than for the low value of Kmax. This mechanism is schematically illustrated in Figure 15.

Conclusions
Rotating and four-point bending fatigue tests were conducted on a fine-grained WC-Co cemented carbide to investigate the FCG behavior of short surface fatigue cracks in detail. Then, the differences in the FCG behavior of short surface fatigue cracks and long through-thickness fatigue cracks were studied. The following conclusions were obtained.
1. There was little effect of the stress ratio on the da/dN-Kmax relation for short surface fatigue cracks. 2. Short surface fatigue cracks have a longer region where fatigue crack growth is stable than long through-thickness fatigue cracks. In other words, long through-thickness fatigue cracks grow in a more brittle and unstable manner than short surface fatigue cracks. The FCG behavior of the short surface cracks is more susceptible to repeated stress than that of long through-thickness cracks. Thus, the FCG behaviors of both types of crack are clearly different. 3. The crack growth paths were classified into four types: (1) within WC grains, (2) within the Co phase, (3) along WC/WC boundaries, and (4) along WC/Co boundaries. The percentage of crack growth paths along WC/WC boundaries decreased from 50 to 30% when Kmax was increased

Conclusions
Rotating and four-point bending fatigue tests were conducted on a fine-grained WC-Co cemented carbide to investigate the FCG behavior of short surface fatigue cracks in detail. Then, the differences in the FCG behavior of short surface fatigue cracks and long through-thickness fatigue cracks were studied. The following conclusions were obtained.

1.
There was little effect of the stress ratio on the da/dN-K max relation for short surface fatigue cracks.

2.
Short surface fatigue cracks have a longer region where fatigue crack growth is stable than long through-thickness fatigue cracks. In other words, long through-thickness fatigue cracks grow in a more brittle and unstable manner than short surface fatigue cracks. The FCG behavior of the short surface cracks is more susceptible to repeated stress than that of long through-thickness cracks. Thus, the FCG behaviors of both types of crack are clearly different.