metals Article
On the Short Surface Fatigue Crack Growth Behavior in a Fine-Grained WC-Co Cemented Carbide Hiroko Mikado 1, *, Sotomi Ishihara 2 , Noriyasu Oguma 3 and Shingo Kawamura 1 1 2 3
*
Machinery and Engineering Group, YKK Corporation, 200 Yoshida, Kurobe, Toyama 938-8601, Japan;
[email protected] National Institute of Technology, Toyama College, 13 Hongo, Toyama 939-8630, Japan;
[email protected] Faculty of Engineering, University of Toyama, 3190 Gofuku, Toyama 930-8555, Japan;
[email protected] Correspondence:
[email protected]; Tel.: +81-80-5981-8105
Received: 28 May 2017; Accepted: 3 July 2017; Published: 6 July 2017
Abstract: 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 Kmax (Kmax = 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 Kmax , WC grain breakage often occurs, since the driving force of FCG is large, and the fatigue crack grows linearly. Keywords: WC-Co cemented carbide; short surface fatigue crack; long through-thickness fatigue crack; fatigue crack growth (FCG); crack growth path; stress intensity factor (SIF)
1. 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].
Metals 2017, 7, 254; doi:10.3390/met7070254
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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 [6–11]. 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 Kmax 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 Kmax 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 Kmax , 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, Kmax , 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.
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2. Material Materials and Methods 2.1. the present study, a commercially available fine-grained WC-Co cemented carbide was used 2.1.InMaterial as the testing material. Tables 1 and 2 show the chemical composition and mechanical properties of In the respectively. present study, a commercially available fine-grained cemented carbide was used the material, The material contains 13.0 wt % Co, andWC-Co its bending strength is 4100 MPa. asYoung’s the testing material. 1 and 2 show the chemical composition andwas mechanical properties The modulus wasTables obtained from the catalog. The fracture toughness the average value of of the material, respectively. The material contains 13.0 wt % Co, and its bending strength is 4100 MPa. five measurements by the single-edge-precracked-beam (SEPB) method [22]. The bending strength The Young’s modulus was obtained from the catalog. The fracture toughness was the average value was the average value of three measurements by the three-point bending test using plane specimens as of five measurements by the3a). single-edge-precracked-beam (SEPB) value method [22]. The bending shown in the next section (Figure The Vickers hardness was the average of ten measurements strength was the average value of three measurements by the three-point bending test using plane performed with a Vickers hardness tester (FUTURE-TECH CORP., Kanagawa, Japan) under a load intime the next (Figure 3a). The hardness the average valueis of of specimens 2.94 N andasa shown holding of 20section s. Figure 1 shows the Vickers microstructure ofwas the material, which ten measurements performed with a Vickers hardness tester (FUTURE-TECH CORP., Kanagawa, a composite microstructure consisting of both a WC and a Co phase. Figure 2a,b shows histograms of undersize a load 2.94 N andfree a holding time of 20 s.constructed Figure 1 shows theJapan) WC grain and of binder mean path, respectively, fromthe themicrostructure observation of of thethe material, which is a composite consisting of both a WC and of a Co 2a,b microstructure shown in Figure 1.microstructure The material has a log-normal distribution WCphase. grain Figure size with shows histograms of the WC grain size and binder mean free path, respectively, constructed from a modal value of about 0.35 µm, and has an exponential distributed binder mean free path ranging the 0observation from to 1 µm. 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 tocomposition 1 μm. Table 1. Chemical of the WC-Co cemented carbide (wt %). Table 1. Chemical composition carbide (wt %). Co Crof the WC-Co W and cemented C 0.51 Cr Bal. Co 13.0 W and C 13.0 0.51 Bal. Table 2. Mechanical properties of the WC-Co cemented carbide. Table 2. Mechanical properties of the WC-Co cemented carbide. Young’s Modulus Fracture Toughness Bending Strength Vickers Hardness Bending Fracture Young’s 1/2 ) (GPa)Modulus (MPamToughness (MPa)Strength (HV) Vickers Hardness (HV) (MPa) (GPa) (MPam1/2) 550 12.1 (11.8–12.6) 4100 (3800–4350) 1480 (1410–1520) 550 12.1 (11.8–12.6) 4100 (3800–4350) 1480 (1410–1520)
WC
Co
1 μm Figure 1. Microstructure of the WC-Co cemented carbide used in the study. The average WC grain Figure 1. Microstructure of the WC-Co cemented carbide used in the study. The average WC grain size size is approximately 0.45 μm. is approximately 0.45 µm.
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Figure 2. Histograms of: (a) WC grain size; (b) Binder mean free path. Figure 2. Histograms of: (a) WC grain size; (b) Binder mean free path. Figure 2. Histograms of: (a) WC grain size; (b) Binder mean free path.
2.2. Specimens 2.2. Specimens 2.2. Specimens The shapes and dimensions of the specimens used in the present study are shown in Figure 3. The shapes and dimensions of the specimens used in the present study are shown in The shapes and dimensions ofspecimens the specimens in the present studyofare shown in Figure Two types of hourglass-shaped withused a minimum diameter 3 mm were used: 3. the Figure 3. Two types of hourglass-shaped specimens with a minimum diameter of 3 mm were 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 used: the un-notched specimen shown in Figure 3a, and the notched specimen shown in Figure 3b. un-notched specimen shown Figure notched shown Figure 3b.the Thelatter former was used to investigate the in S-N curve3a, ofand the the material at aspecimen stress ratio of R in = −1, while was The former was used to investigate the S-N curve of the material at a stress ratio of R = −1, while the 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 latter was used to study the FCG rate of short surface cracks in the material at R = −1. Specimens of used study thetoFCG rate of short surface in thepaste material at R =size −1. of Specimens both types weretopolished a mirror-like finish withcracks diamond (particle 1 μm) toofminimize the both types were polished to a mirror-like finish with diamond paste (particle size of 1 µm) to minimize were polished to a mirror-like finish with diamond paste (particle of 1 μm)specimens to minimize effects of roughness and residual stress. The surface roughness Ra of size the polished wasthe less the effects of roughness and residual stress. The surface roughness Ra of the polished specimens effects of roughness and residual residual stress. The surface roughness Ra of than 0.1 μm. The compressive stress σr on the surface of the thepolished polishedspecimens specimenswas wasless less was less than 0.1 µm. The compressive residual stress σ on the surface of the polished specimens r than The σr on theinsurface the polished specimens was lessan than0.1 500μm. MPa in compressive the WC phaseresidual and lessstress than 200 MPa the Coof phase. For the notched specimen, was500 less than in theand WC phase and than 200 MPa in the phase. For the notched than MPa in500 the MPa WC phase than 200less MPa in the Coand phase. For Co the0.04 notched specimen, an artificial notch with a length of 0.08less mm, a width of 0.02 mm, a depth of mm was introduced specimen, an artificial notch with a length of 0.08 mm, a width of 0.02 mm, and a depth of 0.04 mm 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 wasthe introduced the specimen surfacemachining. by laser beamaddition, machining. In addition, four-point bending into specimeninto surface beam four-point bending fatigue were conducted at R = by 0.1laser using the rectangularInspecimens. Figure 4 shows the shapetests and fatigue tests were conducted at R =the 0.1 rectangular using the rectangular specimens. Figure 4 the shows the shape were conducted at R = 0.1 using specimens. Figure 4 shows shape and dimensions of the specimen, which were 8 mm wide, 4 mm high, and 50 mm long. A Vickers and dimensions the specimen, which were 8 mm wide, 4 mm high, mm long. Vickers dimensions the ofspecimen, 8 mm wide, 4 mm andand 50 50 mm AA Vickers indentationof(indentation load:which 400 Nwere and indentation time 20 s.)high, was introduced onlong. the center of the indentation (indentation load: 400 and indentation time was introduced the center the indentation load: 400 NN and indentation time 2020 s.)s.) was introduced onon the center ofof the specimens (indentation to make a pre-crack. specimens to make a pre-crack. specimens to make a pre-crack.
A A (Depth 0.04)
(mm) (mm)
(a) (a)
(Depth 0.04) Detail of A
(b) (b)
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Detail of A
Figure 3. Specimens used for S-N curve and investigating the fatigue crack growth (FCG) rate of Figure 3. Specimens S-N curve and investigating thespecimen fatigue crack growth (FCG) rate of short cracksused at afor stress = −1: (a) Plane (un-notched specimen) for Figuresurface 3. Specimens used for S-N ratio curve of andRinvestigating the fatigue crack growth (FCG) rate of short short surface cracks at a stress ratio of R = −1: (a) Plane specimen (un-notched specimen) for determination of aS-N curve; for investigating thespecimen) FCG ratefor of determination short surface surface cracks at stress ratio(b) of RNotched = −1: (a)specimen Plane specimen (un-notched determination of S-N curve; (b) Notched specimen for investigating the FCG rate of short surface cracks. of S-N curve; (b) Notched specimen for investigating the FCG rate of short surface cracks. cracks.
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B
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Figure 4. 4. Notched Notched specimens specimens used used for for investigating investigating the the FCG FCG rate rate of 0.1. Figure of short short surface surface cracks cracks at at R R= = 0.1.
2.3. Experimental Experimental Procedure for Fatigue Tests Tests 2.3.1. Rotating Rotating Bending Bending Fatigue Fatigue Tests Tests (R −1) 2.3.1. (R = = −1) Rotating bending bendingfatigue fatiguetests testswere wereconducted conductedinin room temperature a stress Rotating airair at at room temperature at aatstress ratioratio of Rof = R = − 1 with a stress frequency of 10–15 Hz. The un-notched and notched specimens shown in −1 with a stress frequency of 10–15 Hz. The un-notched and notched specimens shown in Figure 3a,b Figurerespectively 3a,b were respectively usedthe to fatigue evaluate the fatigue lifetime the of surface FCG forcracks. short were used to evaluate lifetime and the rate ofand FCG forrate short surface cracks. The fatigue tests on the notched specimen were interrupted periodically to collect The fatigue tests on the notched specimen were interrupted periodically to collect specimen-surface specimen-surface replicas.films Acetylcellulose films and acetone utilized for the replica and the replicas. Acetylcellulose and acetone were utilized were for the replica films and films the solvent, solvent, respectively. The of lengths ofcracks fatiguetranscribed cracks transcribed thesefilms replica films were measured respectively. The lengths fatigue on theseon replica were measured using a using a laser microscope. Two types of FCG test were conducted: FCG tests under constant stress stress laser microscope. Two types of FCG test were conducted: FCG tests under constant amplitudes (increasing-K tests), and FCG tests at a constant K max.. The The rate rate of of FCG, can be be amplitudes (increasing-Kmax max tests), and FCG tests at a constant Kmax FCG, da/dN, da/dN, can obtained from the plot of 2a versus N, where 2a and N are the crack length and the number of stress obtained from the plot of 2a versus N, where 2a and N are the crack length and the number of stress cycles, respectively. respectively. For were determined determined as as cycles, For the the constant constant stress stress amplitude amplitude tests, tests, the the values values of of da/dN da/dN were the slope slope of of the the approximate approximate fitting fitting curve curve to to the the experimental experimental data data at at several several measurement measurement points. points. the On the other hand, for the constant K tests, the values of da/dN were determined as the slope of max 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 K value. the approximate straight lines fitted to the experimental data at each Kmax max value. Figure 5a shows the specimen surface after the laser beam machining. In this figure, Figure 5a shows the specimen surface after the laser beam machining. In discoloration this figure, due to the effect of laser heating can be seen around the notch. It was confirmed that there was some discoloration due to the effect of laser heating can be seen around the notch. It was confirmed that melting of the material as shown in Figure 5b and some cobalt oxidation as shown in Figure 5c in there was some melting of the material as shown in Figure 5b and some cobalt oxidation as shownthe in discolored The heat-affected zoneheat-affected was determined thedetermined discolored region. The total length of Figure 5c inregion. the discolored region. The zoneaswas as the discolored region. the discolored region is about 120 to 140 µm. Figure 5d shows the appearance of a short surface fatigue The total length of the discolored region is about 120 to 140 μm. Figure 5d shows the appearance of a crack that wasfatigue initiated and that grewwas from an artificial To eliminate the effect of To the eliminate heat-affected short surface crack initiated and notch. grew from an artificial notch. the zone, the region used to measure the rate of FCG was set outside the heat-affected zone. effect of the heat-affected zone, the region used to measure the rate of FCG was set outside the On the driving heat-affected zone. force of fatigue cracks in brittle and microscopically heterogeneous materials, a common understanding not yet beeninestablished. In the present study, the maximum stress On the driving force ofhas fatigue cracks brittle and microscopically heterogeneous materials, a intensity factor, K , was utilized, as in previous studies [4,21]. To calculate the K , the following max common understanding has not yet been established. In the present study, themax maximum stress expression was used: intensity factor, Kmax, was utilized, as in previous studies √ [4,21]. To calculate the Kmax, the following K = Yσ πa, (1) max max expression was used: where σmax is the maximum stress, a is a half and Y is the crack shape correction K maxthe = Ycrack σ max length, πa , (1) factor. A value of 0.73 was used for Y assuming that the crack is semicircular [23]. An actual crack where σmax is the maximum is along a half athe crackpath length, anditYusually is the crack does not grow along a straightstress, path, abut zigzag because growsshape alongcorrection a WC/Co factor. A value of 0.73 wasThe used forlength Y assuming thatinthe semicircular [23].was An employed actual crack boundary as shown later. crack projected thecrack stressisloading direction as does not grow along a straight path, but along a zigzag path because it usually grows along a the crack length 2a in this study. WC/Co boundary as shown later. The crack length projected in the stress loading direction was To investigate the crack growth path in detail, FCG tests were conducted at several constant employed the crack length 2a in this study. values of Kas max using the notched specimen in Figure 3b. The stress amplitude σa was adjusted to To investigate crack growth path value in detail, FCGduring tests were conducted at several constant an appropriate valuethe to maintain a constant of Kmax the fatigue tests, since Kmax increases values of K max using the notched specimen in Figure 3b. The stress amplitude σ a was adjusted to the an with the crack length under a constant stress amplitude. The crack growth path was observed on appropriate valueuntil to maintain a constant value ofAfter Kmax during the fatigue tests, since Kmax increases specimen surface the failure of the specimen. the specimen failure, the fracture surface was with the crack length under a constant stress amplitude. The crack growth path was observed on also investigated in detail using an SEM to reveal the crack growth path on the fracture surface. 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.
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A 100 μm
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Actual crack
100 μm Artificial notch
(d)
Figure 5. Example of an artificial notch (a–c) and a short surface fatigue crack initiated from the notch Figure 5. Example of an artificial notch (a–c) and a short surface fatigue crack initiated from the notch (d): (a) Optical microscope image of laser beam machined notch; (b) SEM image of A around the (d): (a) Optical microscope image of laser beam machined notch; (b) SEM image of A around the notch in Figure 5a; (c) The oxygen signal mapping in the exact area of Figure 5b evaluated by energy notch in Figure 5a; (c) The oxygen signal mapping in the exact area of Figure 5b evaluated by energy dispersive X-ray spectrometry (EDS); (d) Appearance of a short surface fatigue crack on a replica dispersive X-ray spectrometry (EDS); (d) Appearance of a short surface fatigue crack on a replica film. film.
2.3.2. Four-Point Bending Fatigue Tests (R = 0.1) 2.3.2. Four-Point Bending Fatigue Tests (R = 0.1) In addition to the rotating bending fatigue tests at the stress ratio R = −1, four-point bending 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 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 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 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 residual stress, on the FCG behavior of short surface cracks, the introduced crack was extended to a a length of approximately 200 µm by applying a cyclic load. A servo-hydraulic fatigue testing machine 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 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 temperature with a stress frequency of 10 Hz. The FCG behavior of short surface cracks was using the replication technique. measured using the replication technique. 3. Results 3. Results 3.1. S-N Curve at R = −1 3.1. S-N Curve at R = −1 The S-N curve was investigated using the un-notched fatigue specimens. Figure 6 shows the S-N The was investigated using the un-notched fatigue 6 shows the curve forS-N the curve fine-grained WC-Co cemented carbide at a stress ratiospecimens. of R = −1. Figure The fatigue limit at 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 Rto=the −1 was estimateddata. to beA1600 MPa. The solid line in the figure an approximate fitting curve experimental fatigue test was conducted using oneshows specimen for each stress amplitude, to the experimental data. A fatigue test was conducted using one specimen for each stress since a statistical analysis on the fatigue life is not the main purpose of this study. amplitude, since a statistical analysis on the fatigue life is not the main purpose of this study.
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0 103
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0 103 Number 104 of
105
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cycles cycles ] 10 10 to failure 10 Nf [ 10 5
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Number of cycles to failure Nf [ cycles ] Figure Figure 6. 6. S-N S-N curve curve for for the the fine-grained fine-grained WC-Co WC-Co cemented cemented carbide. carbide. Figure 6. S-N curve for the fine-grained WC-Co cemented carbide.
3.2. Fatigue Crack Growth (FCG) Behavior Behavior of of Short Short Surface Surface Cracks Cracks 3.2. Fatigue Crack Growth (FCG) Behavior of Short Surface Cracks
The FCG inin thethe WC-Co cemented carbide waswas studied using the FCG behavior behaviorofofshort shortsurface surfacecracks cracks WC-Co cemented carbide studied using The FCG behavior of short surface cracks in the WC-Co cemented carbide was studied using notched Figure 7Figure shows variation of the of crack length 2a as 2a a function of the the notched specimens. Figure 7 shows the of the crack cracklength length 2a a function of the the specimens. notched specimens. 7 the shows thevariation variation the as as a function ofnumber the of cycles N under several conditions at R = − 1. Figure 7a shows the result under a constant stress number of cycles N under several conditions at R = −1. Figure 7a shows the result under a constant number of cycles N under several conditions at R = −1. Figure 7a shows the result under a constant amplitude σ of 600 MPa. Figure 7b,c shows the 2a vs. N relations for constant K values of 6.0 stressstress amplitude σ a of 600 MPa. Figure 7b,c shows the 2a vs. N relations for constant K max values of a max amplitude σa of 600 MPa. Figure 7b,c shows the 2a vs. N relations for constant K max values of 1/2 1/2 1/2 and 7.5 , respectively. The rate ofof FCG, da/dN, the constant-σ obtained 6.0 and 7.5 , respectively. The rate da/dN, underthe theconstant-σ constant-σ test was obtained 6.0MPam andMPam 7.5 MPam , respectively. The rate ofFCG, FCG, da/dN, under under a test waswas obtained aa test from Figure as slope the slope of the approximatefitting fittingcurve curve data, and KmaxKKwas from Figure 7a of approximate the experimental data, and Figure 7a as as7athe the slope ofthe the approximate fitting curveto tothe theexperimental experimental data, and max was max calculated using Equation The valuesof da/dN in in the the constant-K max tests in Figure 7b,c were calculated using Equation (1). The values constant-K tests in 7b,c were using Equation (1).(1). values ofofda/dN da/dN constant-K max tests in Figure max similarly evaluated as the slopes of the approximate straight lines fitted to the experimental data. similarly evaluated evaluated as as the the slopes slopes of of the the approximate approximate straight straight lines lines fitted fittedto tothe theexperimental experimentaldata. data. Figure 8a,b shows the relations between the rate of FCG, da/dN, and the Kmax obtained at stress Figure Figure 8a,b 8a,b shows shows the therelations relationsbetween betweenthe therate rateofofFCG, FCG,da/dN, da/dN,and andthe theKKmax max obtained at stress ratios of R = −1 and 0.1, respectively. In these figures, the experimental results are plotted for the ratios of and 0.1, 0.1, respectively. In In these these figures, the experimental results are plotted for the of R R == − −11 and constant-σa tests (open circles) and the constant-Kmax tests (black and gray solid circles). Focusing on constant-σ and the constant-K tests solid circles). Focusing constant-σ a tests (open circles) circles) and the constant-K max tests (black gray max a the effect of the stress ratio by comparing the results of Figure 8a, and b, little difference due to the stress 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. ratio can be vs. KKmax relations. be seen seen in in the the da/dN da/dN vs. maxrelations. 500
[ μm ]
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(a) σ0.4 a = 620 MPa 0.6
0.8
Number of cycles N [ cycles ] Figure 7. Cont.
(a) σa = 620 MPa
1 [×104]
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Crack length length 2a 2a[[μm μm] ] Crack
250 250
RR==-1-1
da da
dN dN
200 200
1/21/2 const.(6.0 (6.0MPam MPam ΚΚmax )) max==const.
150 150 0.5
11
300 300
Crack Cracklength length2a 2a[[μm μm]]
1.5 1.5
22
Number Number of of cycles cyclesNN[[cycles cycles] ] 1/2 1/2 (b) (b) K Kmax max == 6.0 6.0MPam MPam
5 [×10 [×10]5]
R= R = -1 -1
250 250
da da
dN dN
Κmax = const. (7.5 MPam1/21/2 ) Κmax = const. (7.5 MPam )
200 2001.5 1.5
2 2
2.5 2.5
3 4
3
Number of cycles N [ cycles ] [×10 ]4 Number of cycles N [ cycles ] [×10 ] (c) Kmax = 7.5 MPam1/2 (c) Kmax = 7.5 MPam1/2
Figure 7. Variation of crack length 2a as a function of number of cycles N under several conditions at
Figure 7. Variation of crack length 2a2a asas a function of number Nunder underseveral severalconditions conditions Figure of crack a function number of of cycles cycles N at at 1/2; (c) Kof (b) length Kmax = 6.0 MPam max = 7.5 MPam1/2. R = −1:7.(a)Variation σa = 620 MPa; 1/2 . 1/21/2 1/2. R=− (a) (a) σa σ=a 620 MPa; =6.0 6.0MPam MPam Kmax 7.5 MPam = 620 MPa;(b) (b)KKmax max = ; (c); (c) Kmax = 7.5=MPam R1: = −1:
10-7 10-7
R = -1 R = -1
10-7 10-7
Constant-σa
10-8
da/dN [ m/cycle da/dN [ m/cycle ] ]
da/dN [ m/cycle ] da/dN [ m/cycle ]
10-6 10-6
Constant-σa
10-8
10-8
10-9
10-8 10-9 10-9 10-10 10-10 10-11 3 10-11 3
R = 0.1 R = 0.1
Constant-Kmax
4
5
6
7
8
9 10 1/2
5 Kmax6 [ MPam 7 8 9] 10 1/2 Kmax(a) [ MPam ]
Constant-Kmax
10-10
Constant-Kmax 4
10-9
15
15
Constant-Kmax
10-10
10-11 3 10-11 3
4
5
4
6
7
8
9 10
15
1/2 K 5 max [6MPam 7 8 ] 9 10
15
1/2 K(max b)[ MPam ]
(a) (b) Figure 8. Relations between da/dN and Kmax for short surface fatigue cracks; (a) R = −1; (b) R = 0.1. Figure 8. Relations between da/dN and Kmax for short surface fatigue cracks; (a) R = −1; (b) R = 0.1.
Figure 8. Relations between da/dNPath and Kmax for short surface fatigue cracks; (a) R = −1; (b) R = 0.1. 3.3. Observation of the Crack Growth
3.3. Observation the Crack Growth The crack ofgrowth path was Path investigated in detail for R = −1 and under the constant-Kmax conditions (Figure 7b,c). Special attention was paid the interaction the fatigue crack andmax The crack growth path was investigated in to detail for R = −1between and under the constant-K the microstructure (WC grains and the Co phase), particularly the effect of K max on the FCG The The crack growth path was investigated in detail for R = − 1 and under the constant-K conditions (Figure 7b,c). Special attention was paid to the interaction between the fatiguepath. crack andmax observations were conducted in two ways. First, after interrupting the FCG test, the specimen conditions (Figure 7b,c). Special paidparticularly to the interaction the crack and the microstructure (WC grains attention and the Cowas phase), the effectbetween of Kmax on thefatigue FCG path. The surface was investigated in detail thephase), SEM. Second, thethe failure of of aFCG specimen, its the microstructure (WC grains and the Co particularly effect K test,onthe thefracture FCG path. observations were conducted in using two ways. First, after after interrupting the specimen
3.3. Observation of the Crack Growth Path
max
was investigated in detailinusing SEM. Second, the failurethe of aFCG specimen, its fracture The surface observations were conducted two the ways. First, afterafter interrupting 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
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fracture surface and specimen surface, the same locations of the fatigue specimen were selected for the two observations. Metals 2017, 7, 254 9 of 179a) and Figure 9 shows the observation results for Kmax values of 6.0 MPam1/2 (Figure 1/2 7.5 MPam (Figure 9b). These figures comprise (A) schematic illustrations of the crack growth surface was observed using the SEM. To clarify the relationship between the observations of the path, (B)fracture SEM images specimen surface, and locations (C) SEMofimages of the fracture surface. Labels surface of andthe specimen surface, the same the fatigue specimen were selected for (1–3) are attached to observations. these figures to indicate the same locations in each figure. Some broken lines have been the two Figure9a-B,b-B 9 showstothe observation results for Kmaxofvalues 6.0 MPam1/2 (Figure 9a) and 7.5 added to Figure facilitate the visualization grainofboundaries. 1/2 (Figure 9b). These figures comprise (A) schematic illustrations of the crack growth path, (B) MPam The observed crack growth paths on the specimen surfaces were classified into four types [17]: SEM images of the specimen surface, and (C) SEM images of the fracture surface. Labels (1–3) are (1) within WC grains, (2) within the Co phase, (3) along the WC/WC boundaries, and (4) along the attached to these figures to indicate the same locations in each figure. Some broken lines have been WC/Co boundaries. As can be seen from Figure 9a-A,a-B, at the low Kmax value of 6.0 MPam1/2 , added to Figure 9a-B,b-B to facilitate the visualization of grain boundaries. the crack mainly grew along the WC/WC (3))were among the above four types The observed crack growth paths onboundaries the specimen(type surfaces classified into four types [17]:of crack growth paths. This also be from thethe fracture surface in Figure 9a-C, where (1) within WCfinding grains, can (2) within theconfirmed Co phase, (3) along WC/WC boundaries, and (4) along the many 1/2, the boundaries. As canexist, be seen Figure 9a-A,a-B, at the low Kmax value 6.0 MPamthat missingWC/Co portions of WC grains as from highlighted by the yellow arrows. Thisofindicates the crack crack mainly grew along the WC/WC boundaries (type (3)) among the above four types of crack grew along the WC/WC boundaries at the low value of Kmax . In contrast, at the higher Kmax value of growth paths. This finding can also be confirmed from the fracture surface in Figure 9a-C, where 7.5 MPam1/2 (Figure 9b-A,B), many cleavage fractures of WC grains were observed compared with at many missing portions of WC grains exist, as highlighted by the yellow arrows. This indicates that the low the value of Kmaxalong . This can also be confirmed from the fracture surfaces, where there are many crack grew the WC/WC boundaries at the low value of Kmax. In contrast, at the higher Kmax cleavagevalue faces, as highlighted by the yellowmany arrows in Figure 9b-C.ofThus, the crack within WC 1/2 of 7.5 MPam (Figure 9b-A,B), cleavage fractures WC grains weregrew observed grains more frequently at the of K . In the fatigue crack growth process of cemented compared with at the low higher value of value Kmax. This can also be confirmed from the fracture surfaces, where max there are many cleavage faces, as highlighted by the yellow arrows in Figure 9b-C. Thus, the crack carbides, WC grains form bridging, which is usually formed behind the main crack tip. As indicated grew arrow within in WCFigure grains9b-B, more for frequently at the valueofofbridging Kmax. In the crack growth by the black example, thehigher existence canfatigue be confirmed. It appears process of cemented carbides, WC grains form bridging, which is usually formed behind the main that there is another crack in addition to the main crack. crack tip. As indicated by the black arrow in Figure 9b-B, for example, the existence of bridging can Figure 9 showsIt part of that a crack detail. to The be confirmed. appears there growth is anotherpath crack in in addition the observed main crack. crack growth paths on specimen surfaces with a large area were classified into four types, and thecrack percentages of each Figure 9 shows part of a crack growth path in detail. The observed growth paths on type of specimen surfaces a large at area were classified into four types, andof thethe percentages of each type crack growth path were with evaluated several Kmax values. The results classification are shown in of crack growth were evaluated several Kmax The results the shown classification are Figure 10, in which thepath percentages of the atfour types of values. crack growth pathofare as a function of shown in Figure 10, in which the percentages of the four types of crack growth path are shown as a Kmax . The percentage of type (3) paths, i.e., along the WC/WC boundaries, decreased from 50 to 30% function of Kmax. The percentage of type (3) paths, i.e., along the WC/WC boundaries, decreased from with an 50 increase in K an increase from 6.0 to 7.5 MPam1/2 , whereas the percentage of type (1) paths, i.e., within to 30% with max in Kmax from 6.0 to 7.5 MPam1/2, whereas the percentage of type (1) paths, WC grains, increased from 20 to 40%. i.e., within WC grains, increased from 20 to 40%. Crack growth (A)
within WC grain
(1)
(3)
(2)
within Co phase WC/WC boundary WC/Co boundary
(B)
(1)
(C)
(1)
(3)
(2)
(2)
(3)
1μm
(a) Kmax = 6.5 MPam
1/2
(Low-Kmax)
Figure 9. Cont.
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(3) Crack growth
(A) (A)
(3)
(2)
within WC grain
(2)
within WC grain
(1)
within WC grain
(1)
within WC grain
WC/Co boundary WC/WC boundaryWC/Co boundary WC/WC boundary
(B) (B)
(3)
(3)
bridging
bridging
(2)
(2)
(1)
(1)
(1)(1)
(C) (C)
(2) (2)
(3) (3)
1μm 1μm
(b)KKmax max = 7.5 MPam1/2 (High-Kmax) (b) = 7.5 MPam (High-Kmax) 1/2
Figure 9. Observations of crack growth paths at R = −1. Tests were conducted at a constant value of
percentages of crack growth path [ % ]
percentages of crack growth path [ % ]
Figure 9. Observations of crack growthpaths paths at at R were conducted at a at constant value of Figure 9. Observations crack growth R1/2==; −1. −1.Tests Tests were conducted a constant 1/2; (b) ; (a) Kmax = 6.0 of MPam Kmax = 7.5 MPam (A) Schematic illustrations of the crack growthvalue of Kmax 1/2; (b) Kmax = 7.5 MPam1/2; (A) Schematic illustrations of the crack growth max; (a) Kmax = 6.0 MPam K 1/2 1/2 Kmax ; (a) Kmax 6.0 images MPamof the ; (b) Kmax =surface; 7.5 MPam (A) Schematic illustrations path; (B)=SEM specimen (C) SEM; images of the fracture surface. of the crack growth path; (B) SEM images of the specimen surface; (C) SEM images of the fracture surface. path; (B) SEM images of the specimen surface; (C) SEM images of the fracture surface. 60
60
(iii) WC/WC boundary 50 (iii) WC/WC boundary
(i) within WC grain
50
(i) within WC grain
40
40 30
30
(iv) WC/Co boundary
20
(ii) within Co phase
20
(iv) WC/Co boundary
10
10
0 6
0 6
(ii) within Co phase 7
8 1/2
]
1/2
]
Kmax [ MPam 7
Kmax [ MPam
8
Figure 10. Relationship between percentage of each type of crack growth path and Kmax, observed at R = −1.
Figure 10. Relationship between typeofofcrack crackgrowth growth path , observed at Figure 10. Relationship betweenpercentage percentage of of each each type path andand KmaxK, max observed at R = −1. R = −1.Figure 11 shows SEM images of the fracture surface of an un-notched specimen that failed at σa of 1600 MPa. Figure 11a shows the fracture surface at the low Kmax near the crack origin, and Figure Figure 11the shows SEM images fracture surface of an un-notched that at σa 11b fracture surface at of thethe high Kmax far from the crack origin. Thespecimen Kmax values forfailed surface Figureshows 11 shows SEM images of the fracture surface oflow an un-notched specimen that failed at σa of of 1600 MPa. Figure 11a shows the fracture surface at the K max near the crack origin, and Figure cracks with a half crack length a, were calculated using the following expression, where the crack 1600 11b MPa. Figure 11a shows the fracture surface at the low K near the crack origin, and Figure max origin. The Kmax values for surface 11b showswas themeasured fracture surface the high Kmax far from the crack length from theatcrack origin:
shows the with fracture surface at thea,high thethecrack origin. The Kmax values surface max far from cracks a half crack length wereKcalculated using following expression, where thefor crack cracks withwas a half crackfrom length were calculated using the following expression, where the crack length measured the a, crack origin: length was measured from the crack origin:
√ Kmax = Yσa πa.
(2)
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K max = Yσ a πa .
(2) In this calculation, an internal crack slightly beneath the specimen surface was regarded as In this calculation, an internal crack slightly beneath the specimen surface was regarded as a a surface crack with a semicircular shape. Therefore, a value of 0.73 was used for Y, as used in 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 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 site for the present material was an aggregate of several WC grains or a coarse WC grain slightly beneath the specimen surface [21]. beneath the specimen surface [21]. There is a noticeable difference between the two images in Figure 11. On the fracture surface 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 near the fracture origin in Figure 11a (at the low Kmax), some missing portions of WC grains were also also observed, as highlighted by the red arrows at the low Kmax . In contrast, on the fracture surface observed, as highlighted by the red arrows at the low Kmax. In contrast, on the fracture surface far far from the fracture origin shown in Figure 11b (at the high Kmax ), several cleavage fractures of the from the fracture origin shown in Figure 11b (at the high Kmax), several cleavage fractures of the WC WC grains were observed, as highlighted by the blue arrows. The above observations of the fracture 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. surfaces were in good agreement with the results shown in Figure 10.
1 μm (a) Kmax = 6.5 MPam1/2
1 μm (b) Kmax = 10.5 MPam1/2 Figure Figure11. 11. SEM SEMimages imagesof ofthe thefracture fracturesurface surfaceon onthe theun-notched un-notchedspecimen specimenfailed failedatatσσa aofof1600 1600MPa. MPa. Red arrows show missing portions of WC grains. Blue arrows show cleavage fractures of WC Red arrows show missing portions of WC grains. Blue arrows show cleavage fractures of WCgrains; grains; (a) near the the crack crackorigin origin(at (atthe thelow lowK Kmax););(b) (b)Image Imagetaken takenfarfar from crack origin (a) Image Image taken taken near from thethe crack origin (at (at the max the high K max). high K ). max
3.4. Effect of the Microstructure on the Rate of FCG 3.4. Effect of the Microstructure on the Rate of FCG Figure 12 shows the variation of the rate of FCG, da/dN, for a short surface crack as a function of 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 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. 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 The crack length was measured while the specimen was in the SEM. da/dN was measured in several zones, indicated as (1–5) in the figure. da/dN in zone (3) (the cleavage fracture zone of WC grains)
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zones, indicated as (1–5) in the figure. da/dN in zone (3) (the cleavage fracture zone of WC grains) was was higher thanin that the other zones, indicating the FCG resistance lowest within higher than that theinother zones, indicating that that the FCG resistance waswas lowest within WCWC grains. grains. Crack tortuosity and bridging parts can be seen in zone (4), i.e., at the WC/WC or WC/Co Crack tortuosity and bridging parts can be seen in zone (4), i.e., at the WC/WC or WC/Co boundaries. boundaries. this zonelower was much inzones. the other zones. da/dN in thisda/dN zone in was much thanlower in thethan other Crack growth
(1)
(2)
(3)
WC/WC boundary in Co phase
WC grain
1μm
(4)
(5)
WC/WC boundary
[×10 ] 2 -9
da/dN [ m/cycle ]
(1)
(2)
(3)
(4)
(5)
1
0 0
2
4
6
8
Distance [ μm ] 1/2. 1/2 . Figure rate along alongthe thecrack crackpath pathatata aconstant constant Kmax of 7.0 MPam Figure12. 12.Changes Changesin incrack crack growth growth rate Kmax of 7.0 MPam
Discussion 4.4.Discussion 4.1.Difference Difference in in the the FCG Behavior and Long Through-Thickness Cracks 4.1. BehaviorBetween BetweenShort ShortSurface SurfaceCracks Cracks and Long Through-Thickness Cracks The FCG FCG behavior behavior of thethe present study waswas expected to be The of short short surface surfacecracks cracksobtained obtainedinin present study expected to be different from that of long through-thickness cracks. In the following, the FCG behavior of different from that of long through-thickness cracks. In the following, the FCG behaviorlong of long through-thickness cracks cracks [4] same cemented carbide willwill be compared through-thickness [4] previously previouslyobtained obtainedusing usingthe the same cemented carbide be compared with that of short surface cracks. FCG tests on the long through-thickness cracks were conducted at a at with that of short surface cracks. FCG tests on the long through-thickness cracks were conducted stress ratio of R = 0.1 and at a stress frequency of 10 Hz using CT (Compact Tension) specimens [4]. [4]. a stress ratio of R = 0.1 and at a stress frequency of 10 Hz using CT (Compact Tension) specimens The result is shown in Figure 13. In this figure, the FCG data for long through-thickness cracks The result is shown in Figure 13. In this figure, the FCG data for long through-thickness cracks (stress (stress ratio R = 0.1) obtained by other researchers [14] using a similar fine-grained cemented carbide ratio R = 0.1) obtained by other researchers [14] using a similar fine-grained cemented carbide to that to that used in the present study are also shown. The FCG data can be approximated by straight lines used in the present study are also shown. The FCG data can be approximated by straight lines on the on the logarithmic graph, and the following Paris equations [24] were derived: logarithmic graph, and the following Paris equations [24] were derived: m . da / dN = CKmax (3) m da/dN = CKmax . (3) The power exponent m in the above equation was approximately 2 for short surface fatigue cracks aboutexponent 10 for long through-thickness fatigue Thebut power m in the above equation wascracks. approximately 2 for short surface fatigue cracks It is well known that residual stress on a specimen’s surface strongly affects the crack growth but about 10 for long through-thickness fatigue cracks. behavior, even at small scales such as on thin films. For example, Ghidelli et al. [25] evaluated the It is well known that residual stress on a specimen’s surface strongly affects the crack growth elastic moduli on thin films considering the effect of residual stress. However, when the residual behavior, even at small scales such as on thin films. For example, Ghidelli et al. [25] evaluated the stress varies with time, as in fatigue crack growth, evaluation of the effects of residual stress often elastic moduli on thin films considering the effect of residual stress. However, when the residual stress involves complicated stress analysis. Therefore, there have been very few studies on the FCG of varies withcarbides time, as considering in fatigue crack growth, of the effects of residual stress often cemented the effects of evaluation residual stress. Thus, in this study, to study the involves FCG complicated stress analysis. Therefore, there have been very few studies on the FCG of cemented behavior, the specimen surface was polished to a mirror-like finish to minimize the effects of carbides considering the effects of residual stress. Thus, in this study, to study the FCG behavior, compressive residual stress induced by machining. The obtained data was compared with that of
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theother specimen surface was the polished mirror-like effects of compressive researchers, where effectsto of aresidual stressfinish were to notminimize taken intothe consideration, in contrast to residual stress induced by machining. The obtained data was compared with that of other researchers, in our study. This is the main reason for not considering the effects of residual stress on FCG in this where theMore effectsdetailed of residual stress on were taken consideration, contrast to in our study. This study. research thenot effect ofinto residual stress oninthe FCG behavior of cemented is carbide the mainwill reason for not considering the effects of residual stress on FCG in this study. More detailed be carried out in the future. research on the effect residual theshort FCG surface behaviorfatigue of cemented carbide will be carried out inthe As can be seenoffrom the stress figure,onthe crack has a longer region where thefatigue future.crack grows stably than the long through-thickness fatigue crack. Thus, the FCG behaviors of As surface can be and seenlong fromthrough-thickness the figure, the short surface fatigue crack different. has a longer region where the short fatigue cracks are clearly fatigueThe crack grows stably than thereferred long through-thickness fatigue crack. Thus,tothe FCG behaviors of Kmax value (hereinafter to as Kfc), at which the crack begins grow unstably (da/dN short surface and long through-thickness fatigue cracks are clearly different. > 10−6 m/cycles) was determined to be 10 MPam1/2 for the short surface fatigue crack, compared with Kmax1/2value to as Kfc ), at which crack begins to grow unstably 7.5The MPam for (hereinafter the long referred through-thickness fatiguethecrack. It was found that (da/dN the long − 6 1/2 > 10 m/cycles) wascrack determined 10 MPam for the short surface crack, compared with through-thickness grows to in be a more brittle and unstable mannerfatigue than the short surface fatigue 7.5crack. MPam1/2 for the long through-thickness fatigue crack. It was found that the long through-thickness crack grows in a 13, more and unstable manner thangrowth the short crack. is defined as In Figure thebrittle Kmax value at the fatigue crack ratesurface da/dNfatigue of 10−6 m/cycles − 6 Figure 13,a the Kmax at the fatigue crackasgrowth Kfc In and that at da/dN ofvalue 10−9 m/cycles is defined Kth. rate da/dN of 10 m/cycles is defined −9 m/cycles is defined as K . as Kfc and that at a da/dN of 10 Figure 14 shows the change in the ratio of Kth/Kfc as athfunction of the average thickness of the Co Figure the change in the ratio ofresults Kth /Kfc as a function ofet the phase, λCo14 . Inshows this figure, the experimental obtained by Fryofetthe al.average [12] andthickness by Llanes al.Co [14] phase, λ . In this figure, the experimental results obtained by Fry et al. [12] and by Llanes et al. Co are also plotted. In their studies, similar cemented carbides to that in the present study were [14] used. areTable also 3plotted. In their similar cemented carbides to that in carbides the present study were used. shows the WC studies, grain sizes and Co contents of the cemented whose FCG data were Table 3 shows the WC grain sizes and Co contents of the cemented carbides whose FCG data were plotted in Figure 14. plottedAs in Figure shown14. in Figure 14, the tendency of fatigue susceptibility (Kth/Kfc) in the crack growth As shown in Figureaffected 14, the by tendency of fatigue susceptibility (Kth /Kfcof ) in crack growth behavior is not greatly the difference in the WC-Co components thethe materials. In other 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 words, theseen difference a long through-thickness crack andare a short surface canofbeKclearly clearly even ifbetween the WC-Co components of the materials different. Thecrack values th/Kfc for seen even if the WC-Co components of at the are different. values oflarger Kth /Kthan long of fc forthose long through-thickness fatigue cracks R materials = 0.1 (black solid marks)The were clearly through-thickness fatigue cracks at R = 0.1 (black solid marks) were clearly larger than those of short short surface fatigue cracks at R = −1 and 0.1 (open or gray circles). A clear difference was observed surface fatigue crackstypes at R = 1 andIt0.1 or out gray[14] circles). A clear difference observed between between the both of− crack. is (open pointed that the mode of static was fracture increases as the thevalue bothof 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. KthTherefore, /Kfc increases, and the fatigue behavior is strengthened as the value of K /K decreases. Therefore, th offc short surface cracks is the results in Figures 13 and 14 show that the FCG behavior themore results in Figures 13 and 14 show that the FCG behavior of short surface cracks is more susceptible susceptible to repeated stress than that of long through-thickness cracks. to repeated stress than that of long through-thickness cracks. R = -1 (Short; fine-grained 13%Co alloy) R = 0.1 (Short; fine-grained 13%Co alloy) R = 0.1 (Long; fine-grained 13%Co alloy) [4] R = 0.1 (Long; suitable alloy for fine-grained 10%Co alloy) [14] R = 0.1 (Long; suitable alloy for fine-grained 16%Co alloy) [14] 10-5
da/dN [ m/cycle ]
10-6
Long
10-7 10-8
Short
10-9 10-10 10-11 3
4
5
6
7
8 9 10
Kmax [ MPam1/2 ]
20
Figure 13. FCG rate for several fine grained alloys as a function of Kmax values. Figure 13. FCG rate for several fine grained alloys as a function of Kmax values.
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c
b
d e
da/dN [m/cycle]
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10-6
da/dN da/dN da/dN [m/cycle] da/dN [m/cycle] da/dN [m/cycle] [m/cycle] [m/cycle] da/dN [m/cycle] da/dN [m/cycle]
Fatigue Fatigue Fatigue sensitivity Fatigue sensitivity Fatigue sensitivity sensitivity sensitivity Fatigue sensitivity Fatigue sensitivity K/fc/fcKKfcfc Kth / Kfc KthK/ thKK/fcthKK K/fcththKKK //fcthK th
1 Long -6 a 10 10-6 1 f c 0.6 -6 10-6 d e 1 0.8 g Short bh 10-6 c d e 1 0.8 Long 10-9 10-6 c d e ab 1 0.4 0.8 Long b f 0.6 10-6 d e Kth Kfc 0.8 hab f g c Short Long 0.6 c d e a ● Long ( R = 0.1 ) 1/2 ] -9 0.8 h K [ MPam Long -9 10 g Short max 10 b 0.6 0.2 a f 0.4 -9 -9 h 〇 Short ( R = -1 ) Long 10 g Short f 0.6 K K KDefinition Kfcfc of Kth and Kfc th 0.4 th ha f g Short 10-9 R= 0.6 ● LongShort ( R = (0.1 ) 0.1 ) Kth Kfcfc 1/2 1/2 ] K [ MPam 0.4 th max max h 0.2 10-9 0 g Short ● Long Kth [ MPam Kfc 1/2 1/2 ] 〇 0.3 Short (( R -1 )) R= = 0.1 K 0.4 0.1 0.2 0.4 0.5 max -9 max Definition of K and Kfc 0.20 10 th th ● (( R Kth [ MPam Kfc 1/2 ]fc 〇 Long Short -1 R= = 0.1 0.1) )) K 0.4 Short max Definition of Kth and Kfc 0.2 Binder mean free path λ [μm] 0 ● R Kth [ MPam K 1/2 ] 〇 Long Short (Co -1 R= = 0.1 0.1) )) 0.5 K maxof K fc 0 0.1 0.2 0.3 Short ( 0.4 Definition 0.2 th and Kfc 0 ● R 1/2 ] 〇 Long Short (( 0.4 -1 R= = 0.1 0.1) )) 0.5 Kmaxof[ MPam 0 0.1 0.2 0.3 Definition K 0.2 th and Kfc Binder mean free path λCo [μm] 0.1) ) 0 〇 Short Co ( R = -1 0 sensitivity 0.1 0.2 free 0.3 microstructure 0.4 relationship 0.5 relationship Definition of Kth and KWC-Co Figure 14 and microstructure for fine-grained cemented 14.Fatigue sensitivity and for fine-grained WC-Co fc Binder mean path λCo [μm] 0Fatigue ( 0.4 R = 0.1 ) 0.5 0 0.1 0.2 free path 0.3 Short Binder mean λCo [μm] cemented carbides. 0 carbides. Figure 14 Fatigue and0.2microstructure relationship 0 sensitivity 0.1 0.3 λ [μm] 0.4 0.5 for fine-grained WC-Co cemented Binder mean free path
Co relationship for fine-grained WC-Co cemented Figure 14 Fatigue sensitivity and microstructure carbides. Binder mean free path λCo [μm] Figure 14 Fatigue sensitivity and microstructure relationship for fine-grained WC-Co cemented carbides. Table 3.3.Microstructural properties and fatigue-testing conditions for several cemented Microstructural properties and fatigue-testing conditions forfine-grained several fine-grained 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. cemented carbides. 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. carbides. 3. properties and fatigue-testing conditions for several fine-grained cemented SymbolsTable Shown Co% carbides.Microstructural WC (μm) λCo (μm) KIc conditions (MPam Crack Length Rcemented (-) Reference dproperties Symbols Shown Co% KIc 1/2) for several Symbols Shown Symbols Shown Co% Table and fatigue-testing fine-grained 1/2 Co% %) d (µm) λ (µm) Reference in Figure 143. Microstructural (wt %) (wtddWC carbides. 1/2 WC Co λ K )) Crack Length R 1/2 ) Crack WC (μm) (μm) λCo Co (μm) (μm) KIc Ic (MPam (MPam Crack LengthLength R (-) (-) R (-) Reference Reference inFigure Figure 14Microstructural (MPam in 14 (wt %) Symbols Shown Co% in Figure 14 (wt %) Table 3. properties and fatigue-testing conditions for several fine-grained cemented 1/2 carbides. 1/2) (μm) λCo Crack Length dWC a 13 0.09 KIcIc (MPam12.4 Long R (-) 0.1Reference Mikado et al. [4] WC0.45 Co (μm) in Figure 14aaa (wt Symbols Shown Co% 13 0.09 12.4 Long 0.1 Mikado et 13%) 13 dWC0.45 0.45 12.4 1/2)12.4 Crack Long Mikado et al. al. [4] [4] 0.09 Long 0.1 Mikado [4] carbides. (μm) 0.45 λCo0.09 (μm) KIc (MPam Length R0.1 (-) Reference b 6 1.0 0.093 8.2 Long 0.1 Fry et et al. al. [12] in Figure 14b (wt 66%) 6 1.0 0.093 8.2 Long Fry et [12] Symbols Shown Co% ab 13 0.45 0.09 12.4 Mikado etFry al. b 0.093 8.2 1/2)8.2 Crack Long 0.1 Fry et al. al. [12][4] 1.0 0.093 Long R0.1 0.1 et al. [12] (μm) λCo (μm) KIc (MPam Length (-) Reference dWC1.0 c 6 0.39 0.15 7.5 Long 0.1 Llanes et al. [14] 0.39 0.15 7.5 Llanes [14] in Figure 14b (wt 6%) 6 1.0 0.093 8.2 Long Long 0.1 Fry etet al. [12] Symbols Shown Co% accc 13 0.45 0.09 12.4 Mikado etal. al. [4]et al. [14] 0.39 0.15 7.5 1/2 7.5 Llanes etLlanes al. [14] 0.15 0.1 (μm) 0.39 λCo (μm) KIc (MPam9.1 ) Crack Length R (-) Reference dWC 1.1 10 0.216 Long 0.1 Fry et al. [12] 10 1.1 0.216 9.1 c 0.39 0.15 7.5 Llanes et al. [14] in Figured14d (wt %) b 6 1.0 0.093 8.2 Long 0.1 Fry et al. [12] a 13 0.45 0.09 12.4 Mikado et al. [4] dd 10 10 1.1 1.1 0.216 0.216 9.1 9.1 Long 0.1 Fry et al. [12] 0.50 0.25 9.2 Llanes 10 1.1 0.216 9.1 ed 10 0.50 Long 0.1 0.1 Llanes et al. 0.39 0.150.25 0.25 12.4 7.5 9.29.2 [14] b 6 1.0 8.2 Long Long Fry etet al. [12] aeece 13 0.09 Mikado etal. al. [4]et al. 0.50 0.25 9.2 Llanes etLlanes al. 10 0.45 0.500.093 0.1 [14][14] 13 0.09 Short −1 This ecff f 0.50 0.25 9.2 10 1.1 0.216 9.1 0.39 0.150.09 0.09 12.4 7.5 12.4 [14] b 6 1.0 8.2 Long Short Fry etetwork al.al.[12] 13 0.45 0.09 12.4 Short −1 This work fd 13 0.45 Short 0.1 This work 13 0.45 0.450.093 12.4 −Llanes 1−1 This work g 18 0.45 0.11 13.7 Short −1 et al. [24] 13 0.09 This work ecfg 0.25 9.2 Llanes 10 1.1 9.1 Long Short Fry etet al.al. [12] 6 0.39 0.150.11 0.11 12.4 7.5 13.7 [14] g 18 0.45 0.11 13.7 Short −1 Mikado et al. [24]et al. gd 18 0.45 Short 0.1 Mikado et al. 18 0.50 0.450.216 13.7 −Mikado 1−1 Mikado [24][24] h 13 0.09 12.4 short This work g 18 13 0.45 0.11 13.7 −1 Mikado et al. [24]work Short efh 0.50 0.25 9.2 Llanes et al. [14] d 10 1.1 0.216 9.1 Long 0.1 Fry et al. [12] h 13 0.45 0.09 12.4 short This work 0.45 0.09 0.09 12.4 short 0.1 This h 13 0.45 12.4 short 0.1 This work
h g ef
13 18 10
0.45 0.50
0.09 0.11 0.25
12.4 13.7 9.2
short Short Long
0.1 −1
Thiset work Mikado et al.[14] [24] Llanes al.
In the case of short surface the crack to the microstructure size of [24] the h 13 0.45 fatigue cracks, 12.4 short 0.1 This work gf 18 0.11 13.7 size is closer −1 Mikado et al. InIn the case of short surface fatigue0.09 cracks, the crack size isShort closer to the microstructure the case oflong short surface thecracks. crack size is to the microstructure size of [24] thesize of the h 13 0.45 fatigue cracks, 0.09 12.4 short 0.1 This work g for 18 through-thickness 0.11 13.7 Thus, Short −1 theirMikado et al. material than fatigue itcloser is suspected that FCG property InIn the case of short surface fatigue cracks, the crack size is closer to the microstructure of the the case of short surface fatigue cracks, the crack size is closer to the microstructure size of thesize material than for long through-thickness fatigue cracks. Thus, it is suspected that their FCG property h the 13 through-thickness 0.45 As can0.09 short 0.1fatigue Thisproperty work material than for long fatigue Thus,9,itthe is suspected that their FCG is affected by microstructure. be seen cracks. from12.4 Figure short surface cracks grow 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, itthe is suspected that their FCG property material than formicrostructure. long through-thickness fatigue cracks. Thus, itthe is suspected that their FCG property is affected bythe the microstructure. As be seen from Figure 9, surface fatigue cracks grow is affected by Ascan be seen from Figure 9,short short surface fatigue cracks grow along WC/WC grain interface in a can zigzag manner while bypassing WC grains. Furthermore, as Inthe the case oflong short surface fatigue cracks, thecracks. crack size is9, closer to the microstructure size of the material than for through-thickness fatigue Thus, it is suspected that their FCG property is affected by the microstructure. As can be seen from Figure the short surface fatigue cracks grow is affected by the microstructure. As can be seen from Figure 9, the short surface fatigue cracks grow along the WC/WC grain interface inbridging a zigzag manner while bypassing WC grains. Furthermore, as along the WC/WC grain interface in a zigzag manner while bypassing WC grains. Furthermore, as shown in zone (4) of Figure 12, a effect is expected to occur, in which unbroken hard material than for long through-thickness fatigue cracks. Thus,9, itthe is suspected that their FCG property is affected by the microstructure. As can be seen from Figure short surface fatigue cracks grow along the WC/WC grain interface in a zigzag manner while bypassing WC grains. Furthermore, as along the WC/WC grain interface in a zigzag manner while bypassing WC grains. Furthermore, shown inzone zone (4) (4) ofupper Figure 12, a abridging effect is expected to occur, in which unbroken hard particles connect the and lower faces of the crack. Therefore, the above zigzag growth and shown in of Figure 12, bridging effect is expected to occur, in which unbroken hard is affected by the(4) microstructure. As can be seen from Figure 9, the surface fatigue cracks grow along the WC/WC grain interface a zigzag manner while bypassing WC grains. Furthermore, as inin zone ofupper Figure 12, ainbridging effect is expected to short occur, in which unbroken hard particles connect the and lower faces theeffect crack. the above zigzag and as shown shown zone (4) of Figure 12, azigzag bridging isTherefore, expected to occur, inFurthermore, which unbroken hard bridging effect are more likely produced infaces theof case of short surface fatigue cracks than ingrowth the case of particles connect the upper and lower of the crack. Therefore, the above zigzag growth and along the WC/WC grain interface in a manner while bypassing WC grains. as shown in zone (4) of Figure 12, a bridging effect is expected to occur, in which unbroken hard particles connect the upper and lowerwhich faces the crack. Therefore, theinabove zigzag and bridging effect arethe more likely produced infaces theof case of short surface fatigue cracks than ingrowth theforce case of long through-thickness fatigue cracks, are followed by a decrease the FCG driving at particles connect upper and lower of the crack. Therefore, the above zigzag growth and shown in zone (4) of Figure 12, a bridging effect is expected to occur, in which unbroken hard bridging effect are more likely produced in the case of short surface fatigue cracks than in the case of particles connect the upper and lower faces of the crack. Therefore, the above zigzag growth and bridging effect area more likely produced in the case of short surface fatigue than inmore theforce case of long through-thickness fatigue cracks, which are followed by afatigue decrease in cracks the FCG driving at the crack tip. As result, it can be inferred that short surface cracks will grow stably bridging effect are more likely produced in the case of short surface fatigue cracks than in theforce case at of 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 long through-thickness fatigue cracks, whichthat are short followed by afatigue decrease in the FCG driving at the crack tip. As a result, it can be inferred surface cracks will grow moreforce stably than long through-thickness fatigue cracks. 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 long through-thickness fatigue cracks, which are followed by a decrease in the FCG driving force at crack tip. Asitaaisresult, result, ititcan short surface fatigue will grow thethe crack As canbe beinferred that short surface fatigue cracks willmore grow more stably than long through-thickness fatigue cracks. In atip. metal, wellfatigue known that ainferred short that surface fatigue crack has acracks higher FCG rate than astably long long through-thickness 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 the crack tip. As a result, it can be inferred that short surface fatigue cracks will grow more stably than than long through-thickness fatigue than long fatigue cracks. In athrough-thickness metal, it is well known that alow short surface fatiguefactor crackrange has a ΔK. higher FCG rate thanfatigue a long through-thickness at inferred acracks. stress intensity Awill short surface thethrough-thickness crack tip. Asitaisfatigue result, itcrack can be that short surface fatigue cracks grow more stably than long through-thickness fatigue cracks. long fatigue cracks. In a metal, well known that a short surface fatigue crack has a higher FCG rate than through-thickness fatigue crack at a low stress intensity factor range ΔK. A short surface fatigue In long awill metal, is well known that a short fatigue crack factor has a range higher than a long crack also itgrow under the threshold levelsurface of the stress intensity ΔKFCG th aa long long th forrate than through-thickness fatigue cracks. In a metal, it is well known that a short surface fatigue crack has a higher FCG rate than a through-thickness fatigue crack at athe low stress intensity factor range ΔK. A shortcarbide surface fatigue In awill metal, isfatigue well known that apresent short surface fatigue crack has arange higher FCG rate thanfatigue a long crack also it grow under the threshold level of the stress intensity factor ΔK th for a long long through-thickness fatigue crack. In study, FCG data on the cemented have not through-thickness crack at a low stress intensity factor range ΔK. A short surface Inwill a metal, it isfatigue well known that alow short surface fatigue crack has a factor higher FCG rate thanfatigue a long through-thickness crack at athe stress intensity factor range ΔK. A range short surface crack also grow under the threshold level of the stress intensity ΔK th for a long through-thickness fatigue crack. In present study, FCG data on the cemented carbide have not through-thickness fatigue crack at a low stress intensity factor range ∆K. A short surface fatigue been systematically obtained in low fatigue crack rate range range, thusAthe difference between crack will under thethe threshold level ofgrowth the stress intensity factor range ΔK th for a long through-thickness fatigue crack at athe low stress intensity factor ΔK. short surface fatigue crack willalso alsogrow grow under the threshold level of the stress intensity factor range ΔK th for a long through-thickness fatigue crack. Incracks 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 and long through-thickness cracks at the low values of K max crack will also grow under the threshold level of the stress intensity factor range ∆K for a long max th cracksystematically will also grow under the threshold levelcrack of study, the stress intensity factor range ΔKth for a long through-thickness fatigue crack. In the present FCG data on thethe cemented carbide have not through-thickness fatigue crack. Incracks the present study, FCG data on the cemented carbide have not been obtained in the low fatigue growth rate range, thus difference between the FCG behavior of short surface and long through-thickness cracks at the low values of K max has not yet been clarified. Further study onpresent this issue isFCG required. through-thickness fatigue crack. In the study, FCG data on the cemented carbide have not through-thickness fatigue crack. In the present study, data on the cemented carbide have not been systematically obtained in the low fatigue crack growth rate range, thus the difference between been systematically obtained in the low fatigue crack growth rate range, thus the difference between the behavior of short Further surface study crackson and long through-thickness cracks at the low values of Kmax has FCG not yet been clarified. this issue is required. been systematically obtained in the low fatigue crack growth rate range, thus the difference between been systematically in the low fatigue crack growth rate range, thus difference the FCG behavior ofobtained short Further surface cracks and long through-thickness cracks at the low values Kmax between the FCG of short surface cracks and long cracks atthe the lowofvalues of Kmax has notbehavior yet clarified. study on this isthrough-thickness required. 4.2. Effect of been the Maximum Stress Intensity Factor, Kissue max max, on the Crack Growth Path the FCG behavior of short short Further surface cracks and long through-thickness crackscracks at the low values ofvalues Kmax of Kmax the FCG behavior of surface cracks and long through-thickness at the low has not yet been clarified. study on this issue is required. the Maximum Intensity Factor, Kmaxissue , on theisCrack Growth Path has4.2. notEffect yet of been clarified.Stress Further study on this required. not yet been clarified. Further study on thisgrowth ispath, required. To consider the effectStress of Kmax on the Factor, crack the size of the plastic zone rpp at the crack max 4.2. Effect of the Maximum Intensity Kissue maxissue , on the Growth Path hashas not yet been clarified. Further study on this isCrack required. To calculated consider the effectStress of Kmax on the Factor, crack growth the size of the plastic zone rp at the crack tip was using 4.2. Effect of the Maximum Intensity Kmax, onpath, the Crack Growth Path 4.2.4.2. Effect ofofthe Stress Intensity Factor, ,the onCrack the size Crack Path To calculated consider the effectStress of Kmax on the Factor, crack growth the of Growth the plastic zone rp at the crack tip was using Effect theMaximum Maximum Intensity KmaxK, max onpath, Growth Path 4.2. Effect of the Maximum Factor, Kmax , on thesize Crack Growth Path 22 the To calculated consider the effectStress of KmaxIntensity on the crack growth path, of the plastic zone rp at the crack tip was using K 2 1growth consider effect ofKKmax max the crack path, theofsize the plastic zone rp (4) at the crack max To considerthe the effect of onon the crack growth path, the size the of plastic zone rp at the crack max tipTo was calculated using r = , p To consider the effect of Kmax on the crack 1 growth p 2path, the size of the plastic zone rp at the crack Kσmax was calculatedusing using (4) tiptip was calculated rp = 2π y y 2 , 1 Kσmax tip was calculated using (4) rp = 2π Ky 2 , 1 , 22 max (4) rp = 2π yK 1 Kσmax max 1 rpp ==2π 1σ y Kmax , (4) (4) , (4) rp2π =2π σ y σy , 2π σ
y
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where σy is the yield strength of the material, which is unknown at present. Thus, the bending strength where σy in is Table the yield strength of theofmaterial, is unknown at present. theeach bending indicated 2 was used instead the yieldwhich strength. The calculated values Thus, of rp for value strength indicated Table 4.2 The was calculation used instead of the yieldzone strength. calculated values of paper rp for of Kmax are shown in Table of the plastic size atThe the crack tip used in this each value of only Kmax to area shown in Table 4. The calculation of the plastic zone size was at the crack tip used is applicable single-phase material. However, this calculation method applied to easily in this paper is applicable a single-phase material.Similar However, thiswere calculation methodinwas obtain the plastic zone sizeonly at thetocrack tip in the material. results also obtained the applied to easily obtain the plastic zone Method) size at theanalysis crack tipreflecting in the material. Similar results wereofalso two-dimensional FEM (Finite Element the actual microstructure the obtained the two-dimensional FEM (Finite Element Method) analysis reflecting the actual cemented in carbide. microstructure of the cemented carbide. Table 4. Plastic zone sizes at the crack tip calculated for several values of Kmax .
Table 4. Plastic zone sizes at the crack tip calculated for several values of Kmax. rp (µm) Kmax (MPam1/2 ) Kmax (MPam1/2) rp (μm) 6.0 0.34 0.340.40 6.5 6.0 0.400.46 7.0 6.5 0.460.53 7.5 7.0 7.5 0.53
The zone rrpp at the crack crack tip tip increases increaseswith withKKmax max as expected. At the the low low KKmax max of The size size of the plastic zone of 1/2 1/2 6.0 MPam , r p of 0.34 μm is smaller than the average WC grain size (0.45 μm) of the present alloy. In 6.0 MPam , rp of 0.34 µm is smaller than the average WC grain size (0.45 µm) of the present alloy. this case, it isitdifficult forfor a crack to to grow within WC grains, i.e., In this case, is difficult a crack grow within WC grains, i.e.,for fortransgranular transgranularcracking crackingtotooccur. occur. Instead, WC/WC interfaces. Instead, the the crack crack is is expected expected to grow preferentially along the weak WC/WC interfaces. On On the the other other 1/2 1/2 hand, at the high K max of 7.5 MPam , r p of 0.53 μm is larger than the average WC grain size. In hand, at , rp of 0.53 µm is larger than the average WC grain size. In this this max of 7.5 MPam case, a low value ofof Kmax . It . case, the thecrack crackgrows growswithin withinWC WCgrains grainsand andtends tendstotobebestraighter straighterthan thanthat thatfor for a low value Kmax grows more rapidly because ofof the It grows more rapidly because thehigher highercrack crackdriving drivingforce forceand andthe thefewer fewerbridging bridgingparts partsthan than for for the . .This the low low value value of of K Kmax Thismechanism mechanismisisschematically schematicallyillustrated illustratedininFigure Figure15. 15. max Crack growth
Crack growth
Bridging parts
Cleavage fracture of WC grain
Crack WC
Co
(a)
(b)
Figure 15. Schematic illustration of the effect of Kmax on the FCG path: (a) at low Kmax (WC/WC Figure 15. Schematic illustration of the effect of Kmax on the FCG path: (a) at low Kmax (WC/WC interface, bridging parts); (b) at high Kmax (cleavage fracture of WC grains). interface, bridging parts); (b) at high Kmax (cleavage fracture of WC grains).
5. Conclusions 5. Conclusions Rotating and four-point bending fatigue tests were conducted on a fine-grained WC-Co Rotating and four-point bending fatigue tests were conducted on a fine-grained WC-Co cemented cemented carbide to investigate the FCG behavior of short surface fatigue cracks in detail. Then, the carbide to investigate the FCG behavior of short surface fatigue cracks in detail. Then, the differences differences in the FCG behavior of short surface fatigue cracks and long through-thickness fatigue in the FCG behavior of short surface fatigue cracks and long through-thickness fatigue cracks were cracks were studied. The following conclusions were obtained. 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 1. cracks. There was little effect of the stress ratio on the da/dN-Kmax relation for short surface fatigue cracks. 2. Shortsurface surfacefatigue fatiguecracks crackshave haveaalonger longerregion regionwhere wherefatigue fatiguecrack crack growth growth is is stable stable than than long long 2. Short through-thicknessfatigue fatiguecracks. cracks.In Inother otherwords, words,long longthrough-thickness through-thicknessfatigue fatigue cracks cracks grow grow in in through-thickness a more brittle and unstable manner than short surface fatigue cracks. The FCG behavior of the a more brittle and unstable manner than short surface fatigue cracks. The FCG behavior of the shortsurface surfacecracks cracksisismore more susceptible susceptibleto to repeated repeated stress stress than than that that of of long long through-thickness through-thickness short cracks.Thus, Thus,the theFCG FCGbehaviors behaviorsof ofboth bothtypes typesof ofcrack crackare areclearly clearlydifferent. different. cracks. 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
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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 from 6.0 MPam1/2 to 7.5 MPam1/2 , while the percentage of transgranular cracks within the WC grains increased from 20% to 40%. At low values of Kmax , it is not easy for a crack to grow within WC grains (transgranular cracking). Instead, fatigue crack growth occurs discontinuously along weak WC/WC interfaces or along WC/Co boundaries. On the other hand, at high values of Kmax , cleavage fractures of WC grains are more common and the area in which cleavage fractures occur is wider than at low values of Kmax . Moreover, cracks tend to be straighter than those for a low Kmax . Thus, cracks grow more rapidly for a high Kmax because of the higher crack driving force and the fewer bridging parts.
Acknowledgments: The authors thank students and research assistants at University of Toyama for their contributions during the experimental work. Most of the research in this article was supported and financed by YKK Corporation. Author Contributions: Hiroko Mikado carried out most of the experimental work and wrote the article. Sotomi Ishihara conceived and designed the experiments and the data analysis. All authors contributed to improving the manuscript. Conflicts of Interest: The authors declare no conflict of interest.
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