Fatigue mechanics of WC–Co cemented carbides

Fatigue mechanics of WC–Co cemented carbides

International Journal of Refractory Metals & Hard Materials 19 (2001) 341±348 www.elsevier.com/locate/ijrmhm Fatigue mechanics of WC±Co cemented carb...

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International Journal of Refractory Metals & Hard Materials 19 (2001) 341±348 www.elsevier.com/locate/ijrmhm

Fatigue mechanics of WC±Co cemented carbides Y. Torres, M. Anglada, L. Llanes

*

Departament de Ci encia dels Materials i Enginyeria Metalál urgica, ETSEIB, Universitat Polit ecnica de Catalunya, 08028 Barcelona, Spain Received 5 March 2001; accepted 18 June 2001

Abstract The fracture and fatigue behavior of a ®ne-grained WC±10 wt% Co hardmetal is investigated. Mechanical characterization included ¯exural strength and fracture toughness as well as fatigue limit and fatigue crack growth (FCG) behavior under monotonic and cyclic loads, respectively. Considering that fatigue lifetime of cemented carbides is given by subcritical crack growth of preexisting defects, a linear elastic fracture mechanics (LEFM) approach is attempted to assess fatigue life±FCG relationships for these materials. Following the experimental ®nding of an extremely high dependence of FCG rates on the applied stress intensity for the hardmetal studied, the LEFM analysis is concentrated, from a practical design viewpoint, on addressing the fatigue limit±FCG threshold correlation under in®nite fatigue life conditions. Thus, fatigue limit associated with natural ¯aws is estimated from FCG threshold experimentally determined for large cracks under the assumptions that (1) similitude on the FCG behavior of small and large cracks applies for cemented carbides, and (2) critical ¯aws are the same, in terms of nature, geometry and size, under monotonic and cyclic loading. The reliability of this fatigue mechanics approach is sustained through the excellent agreement observed between estimated and experimentally determined values for the fatigue limit under the di€erent load ratios investigated. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Fatigue crack growth; Fatigue limit; Fracture mechanics; Cemented carbides

1. Introduction It is now common knowledge that linear elastic fracture mechanics (LEFM) represents a quite e€ective analytical approach for rationalizing the fracture behavior of cemented carbides, materials usually referred to as hardmetals too. This is mainly the result of extensive research conducted on this ®eld over the past three decades, following the pioneering work of Kenny [1], Chermant et al. [2], Exner et al. [3], Lueth [4], and Ingelstr om and Nordberg [5]. Within the LEFM framework, rupture of these brittle materials is considered as being governed by unstable propagation of preexisting ¯aws, a condition characterized by the corresponding critical value of the stress intensity factor, e.g., the plane strain fracture toughness of the material. On the other hand, studies where LEFM is implemented for describing fatigue crack growth (FCG) behavior of cemented carbides are scarce [6±10]. * Corresponding author. Tel.: +34-93-401-1083/6706; fax: +34-93401-6706/6600. E-mail address: [email protected] (L. Llanes).

Moreover, in most of them LEFM application is simply con®ned to discern microstructural or load ratio e€ects on FCG behavior rather than to assess a correlation between FCG resistance and fatigue life. Considering that subcritical crack growth is widely accepted as the controlling stage in the fatigue failure of hardmetals, particularly after the well-organized research conducted by Sockel's group [11±14] in recent years, such a knowledge should be conceived as of primary importance if performance of cemented carbides in fatiguelimited applications, from both design and material selection viewpoints, wants to be optimized. The present work is undertaken to attain a better mechanistic understanding of the fatigue phenomena in cemented carbides. In doing so, LEFM is employed to characterize FCG behavior in both stable (Paris-like) and near-threshold regions in a ®ne-grained WC±Co hardmetal as a function of load ratio. Aiming to assess FCG±fatigue life relationships, emphasis is placed in de®ning critical crack size in terms of the fatigue threshold. A strict damage tolerance analysis is not attempted because the extremely large power-law dependence of crack growth rates on stress intensity exhibited

0263-4368/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 3 - 4 3 6 8 ( 0 1 ) 0 0 0 3 2 - 4

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Nomenclature

C; m; n

Symbols and de®nitions acr critical half-¯aw size da=dN FCG rate KIc plane-strain fracture toughness Kmax maximum stress intensity factor Kth threshold maximum stress intensity factor DK stress intensity factor range

ra rf

by the hardmetal studied. Following these guidelines, fatigue limits are then predicted assuming similitude on the characterization of FCG threshold through fracture mechanics parameters for both long and small cracks. The reliability of such a procedure is ®nally evaluated through direct comparison of estimated and experimental fatigue limit values, the latter ones determined in specimens containing processing ¯aws exclusively and fatigue tested under similar loading conditions to those used in the FCG study.

2. Experimental procedure The cemented carbide used in this investigation was a WC±Co commercial grade with nominal composition of 10 wt% Co and mean WC grain size of 0.8 lm. It was supplied in the form of 45 mm in-length bars with two di€erent rectangular sections. Mechanical characterization included ¯exural strength, fracture toughness, fatigue limit and FCG behavior. Testing in all the cases was conducted under four-point bending by means of a fully articulating test jig with inner and outer spans of 20 and 40 mm, respectively. Strength under monotonic and cyclic loads was evaluated on 45  4  3 mm3 beams. The tested specimens were ®rst diamond ground and polished to mirrorlike ®nish on the surface which was later subjected to the maximum stress in bending. Further, the edges of these samples were slightly chamfered in order to reduce their possible role as stress raisers and fracture origins. Flexural strength was determined as the mean value of ten experiments. These were performed using a servohydraulic testing machine at an applied loading rate of 100 N/s. Fatigue limit, de®ned as the fatigue strength corresponding to an ``in®nite'' life of 107 cycles, was determined following the staircase or up-and-down method [15] using a large enough number of specimens. Experiences were carried out employing a resonant testing machine at working frequencies of about 170 Hz. Three di€erent load ratio, R, values (0.1, 0.4 and 0.7) were studied.

rf rm rr Dr

material constants within equation da= m n dN ˆ C…Kmax † …DK† stress amplitude fatigue limit under non-zero cyclic mean stress fatigue limit under zero cyclic mean stress mean stress ¯exural strength stress range

Crack growth experiences were performed using single edge notched beams (SENB) of 45  10  5 mm3 dimensions with a notch length-to-specimen width ratio, a=W , of 0.3. In these cases, the side surfaces of the specimens were polished to optical ®nish to facilitate crack size assessment. The samples were ®rst precracked by cyclic compression and the resulting cracks were then subjected to far-®eld cyclic tensile loads in order to relieve residual stresses induced by the precracking procedure [16]. Fracture toughness was ®nally determined by testing the precracked SENB specimens to failure under constant loading rate values, between 200 and 400 N/s, and using the stress intensity factor given by Tada et al. [17]. FCG behavior was determined following a direct-measurement method. Tests were run under load control using a sine waveform, at working frequencies ranging from 0.5 to 8 Hz, in a servohydraulic testing machine. FCG at three individual R values (0.1, 0.4 and 0.7) was investigated. Stable crack extension was monitored in situ using a high resolution (5 lm) telescope. Finally, after mechanical testing selected specimens were taken and subjected to a detailed fractographic examination under scanning electron microscopy (SEM). In doing so, special attention was paid to discern nature, geometry and size of strength-limiting ¯aws as well as fracture micromechanisms associated with the di€erent loading conditions studied.

3. Results and discussion 3.1. Flexural strength, fracture toughness and related fractography Mean ¯exural strength, rr , and fracture toughness, KIc , values for the ®ne-grained cemented carbide invesp tigated were p 2742 MPa (130 MPa) and 9.2 MPa m (0.1 MPa m), respectively. They are within the range of those usually reported in the literature for WC±Co hardmetals with similar binder content and carbide grain size, e.g., see [18]. On the other hand, an extended fractographic analysis indicated subsurface processing heterogeneities: pores, abnormally large carbides (Fig. 1),

Y. Torres et al. / International Journal of Refractory Metals & Hard Materials 19 (2001) 341±348

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Fig. 1. SEM micrograph of an abnormally coarse carbide identi®ed as failure initiation site in a sample tested to rupture under monotonic loading.

Fig. 3. FCG rate as a function of: (a) DK; (b) Kmax , for each loading condition investigated. Fig. 2. SEM micrograph showing fractographic aspects associated with monotonic loading in the WC±Co hardmetal studied.

binderless carbide clusters and discrete WC±Co agglomerates as usual fracture initiation sites in the ¯exural strength tests [19]. These critical ¯aws were irregular in shape with size ranging between 8 and 14 lm, the latter values given in terms of diameter of a circular ¯aw whose cross-sectional area is equivalent to that measured for the real defect [16,19]. Finally, dimpled ductile rupture in the metallic binder interdispersed with cleavage and intergranular fracture of the carbides (Fig. 2) were the relevant fractographic features discerned in the surfaces of broken notched specimens, in agreement with previous investigations on the subject (e.g., see [20]). 3.2. Fatigue crack growth (FCG) Taking into account the intrinsic brittle character of cemented carbides, a LEFM-based description of crack growth behavior under cyclic loads was attempted in terms of both stress intensity factor range, DK, and maximum stress intensity factor, Kmax , as it has been shown to apply for other brittle-like materials such as structural ceramics [21,22] or intermetallics [23]. The corresponding FCG rate versus DK and Kmax plots, including data for all the R values studied, are given in Figs. 3(a) and (b), respectively. Several observations can

be highlighted. First, as already known for WC±Co hardmetals [6±8], there exists a very large power-law dependence of crack growth rates on DK (and Kmax ). This is a noticeable setback for implementing a damage tolerance analysis for fatigue life prediction in these materials because small di€erences in the applied stress under consideration could result in quite large ¯uctuations in the estimated fatigue life. Second, although load ratio e€ects on the FCG behavior are observed independently of the fracture mechanics parameter used for describing it, they are largely (although not completely) eliminated when crack growth data is plotted versus Kmax . This translates in a much higher dependency of FCG on Kmax than on DK, similar to what is found for ceramics and intermetallics, and points out signi®cant mean stress e€ects on the fatigue characteristics of cemented carbides. The relative predominance of each fracture mechanics parameter may be quanti®ed by considering that Kmax ˆ DK=…1 R†; and thus, explicitly including both parameters in a modi®ed Paris±Erdogan growth relationship of type da ˆ C…Kmax †m …DK†n ; dN

…1†

where C; m and n are constants. Thus, factoring out a n constant …1 R† from each data set in Fig. 3(b), a best ®t n value may be determined for which all data are

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collapsed onto a single curve. For the hardmetal here studied, this is achieved for n ˆ 5 (Fig. 4) and it yields a regression ®t slope value of 29 (i.e., m ˆ 24). The m  n experimental ®nding clearly sustains the referred strong dependence of FCG rates on Kmax . Third, threshold values, Kth , de®ned as the Kmax associated with a da=dN of 10 9 m/cycle, are directly proportional to the load ratio (Fig. 3(b)), i.e., for a given Kmax , resistance to FCG initiation increases with decreasing applied DK. This correlation allows to indicate Kmax dominance as signi®cant but not unique, because FCG behavior is also found to be dependent, although only moderately for the hardmetal investigated, on the alternating stress intensity. Individual FCG thresholds and exponents in the power-law dependence, both in terms of Kmax , for each load ratio studied are given in Table 1. Fractographic examination did not allow to discern, in agreement with previous work [6±8], remarkable differences on the fracture surface appearance associated with stable and unstable crack growth, especially in terms of clear fatigue-related peculiarities such as striations or spaced markings. However, as it is shown in Figs. 5(a) and (b), with increasing load ratio at constant Kmax ductile dimpled fracture of the metallic binder was more sharply de®ned, providing additional support to the dominance of static modes of fracture during FCG in the cemented carbide studied. Since it is well established that mechanical degradation under cyclic loads in WC±Co hardmetals is concentrated in the cobalt phase [12,24], the observed prevalence of static fracture modes

Fig. 4. Normalized FCG rate as a function of Kmax . Coecients m and n refer to power-law exponents in Eq. (1). Table 1 Summary of the experimental FCG data, in terms of Kmax , for the di€erent load ratios studied Load ratio

Fatigue threshold p (MPa m)

Power-law exponent

0.1 0.4 0.7

6.0 6.5 7.6

24 27 43

Fig. 5. SEM micrographs showing fractographic aspects associated with stable cyclic crack growth under di€erent loading conditions: (a) R ˆ 0:1; (b) R ˆ 0:7.

associated with FCG might be understood, following the ideas proposed for explaining an alike behavior in temper embrittled low alloy steels at high DK levels [25], on the basis of the e€ective low ductility intrinsic to the metallic binder resulting from the severe deformation constraints imposed on it by the surrounding hard WC particles. Consequently, it could be speculated that relative prevalence of static and cyclic fracture modes during FCG in cemented carbides should be markedly dependent upon microstructural parameters, particularly binder mean free path and carbide contiguity. Considering that large dependencies of crack growth rate on DK and marked in¯uence of mean stress on the FCG behavior of structural materials are often ascribed to the existence of additional static modes of fracture during cyclic crack growth [23,25±28], further systematic studies aiming to get a more complete knowledge about the envisaged microstructural e€ects seem required from the standpoint of property-tailoring of hardmetals through microstructural design. 3.3. Fatigue limit±FCG threshold correlation The main goal of this investigation is to assess FCG± fatigue life relationships that could optimize proper design and material selection in fatigue-limited applications involving cemented carbides. Although this might be attempted following a damage tolerance

Y. Torres et al. / International Journal of Refractory Metals & Hard Materials 19 (2001) 341±348

methodology, it does not seem to be an amenable route because the enormous prediction uncertainties associated with marked power-law dependence of FCG rates on Kmax (or DK) as that exhibited by hardmetals. Instead, a more classical and conservative approach on the basis of fatigue limit and FCG threshold, i.e., from an in®nite fatigue life viewpoint, appears to be more appropriate for these materials. This approach is here implemented by simply de®ning critical ¯aw size under cyclic loading in terms of FCG threshold. Under this consideration, fatigue limit, rf , would then be given by the maximum stress, rmax (or stress range, Dr) resulting in the threshold intensity factor, Kth , of a small nonpropagating crack emanating from a defect of critical size, 2acr , according to relationships of type Kth rf / p : acr

…2†

Hence, rf values could be predicted using the experimental ®ndings reported in previous sections provided that the fundamental LEFM correlation among defect size, strength and threshold conditions evaluated for large cracks applies for natural ¯aws too. Although it is well known that in many metallic and advanced ceramic materials FCG of small cracks di€ers considerably from that of large cracks, particularly within the subthreshold regime (e.g., see [29]), such anomalous behavior should not be expected in cemented carbides. This statement may be asserted considering that: (1) size of processing ¯aws is several times the mean carbide grain size, the characteristic microstructural unit of these materials; (2) near-tip plasticity is con®ned to a zone process whose extension is about the binder mean free path [20,30], i.e., it is also much smaller than size of natural ¯aws; and (3) multiligament zone behind the crack tip where crack shielding due to ductile-phase bridging takes place consists of only between two and four metal ligaments [20,30], i.e., di€erences in crack growth resistance between large and small cracks, from bridging zone development as crack size increases, are not expected to be signi®cant. Table 2 lists predicted fatigue limit values for each load ratio investigated. They are given in terms of maximum stress and were directly estimated from Table 2 Predicted and experimentally determined fatigue limit values, in terms of maximum applied stress, for the di€erent load ratios investigated Load ratio

Observed fatigue limit (MPa)

Predicted fatigue limit (MPa)

0.1 0.4 0.7

1827  92 1783  70 2112  70

1788 1937 2265

 rf ˆ

 Kth rr KIc

345

…3†

under the assumption that strength-controlling ¯aws are the same, with respect to type, geometry, size and distribution under monotonic and cyclic loading. This latter hypothesis has been shown to apply for other hardmetals and cermets [13] and is also experimentally supported in this work through fractographic examination by SEM, as it will be seen later. From Eq. (3), it is interesting to note the explicit equivalence resulting from using strength or crack growth critical parameters, i.e., rf =rr or Kth =KIc , respectively, for describing fatigue sensitivity in cemented carbides. Indeed, such a correlation should not be considered as unexpected because it is implicit to the basis sustaining the whole analysis: (1) initiation of subcritical crack growth as the controlling stage in the fatigue failure phenomena; and (2) similitude on the fatigue threshold behavior of large and small cracks. In order to check the validity of the analysis, fatigue limits were experimentally determined through testing unnotched and smooth specimens under similar conditions (bending, load ratios) to those used for the FCG study, and failure origins of all broken samples were examined by means of SEM. For evaluating fatigue limits, up-and-down fatigue tests to groups of more than 15 samples were performed for each R value. The complete testing sequences are shown in Fig. 6. After statistical analysis of the experimental data, mean and standard deviation values for the fatigue limit were determined and the 95% con®dence values are listed in Table 2. Overall, the agreement between predicted and observed fatigue limits must be described as excellent, with errors relative to the experimental values always lower than 10%, a ®nding that yields strong support to the FCG threshold±fatigue limit correlation proposed in this study. On the other hand, the fractographic study conducted on specimens that experienced fatigue failure revealed that the corresponding origins were of same type, shape and size as those already discerned as strength-controlling ¯aws under monotonic conditions. An illustrative example is given in Fig. 7 where a subsurface spherical-like pore of size about 10 lm in diameter is clearly discerned as the critical ¯aw. This clearly sustains prediction of fatigue limits from FCG sensitivity directly, i.e., implementing Eq. (3). Finally, the estimated and experimental data given in Table 2 may be used to evaluate R e€ects on fatigue limit. In doing so, predicted values were plotted in terms of stress amplitude …ra † and mean stress …rm †, as shown in Fig. 8. Fitting of the data to a linear relationship (including measured ¯exural strength for ra ˆ 0) is extremely good, suggesting a Goodman-like relation to hold for the cemented carbide investigated. The

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Fig. 8. Description through a Goodman-like diagram of mean stress e€ects on the fatigue limit of the WC±Co hardmetal studied.

 ra ˆ

Fig. 6. Up-and-down fatigue tests used to determine mean fatigue limits under di€erent load ratios for the cemented carbide investigated.

rf

1

 rm ; rr

…4†

where rf corresponds to the fatigue limit under zero cyclic mean stress …R ˆ 1†. Best ®t of the predicted fatigue limit data, according to Eq. (4), yields a slope of )0.44 and is graphically shown in Fig. 8. As expected, from the concordance already observed between experimentally determined and estimated fatigue limit values, description of experimental failures and runouts by the drawn failure locus is fairly good. Furthermore, a comparison of the fatigue sensitivity estimated for R ˆ 1 from the curve-®tting performed (just the slope value) with data available in the literature indicates that it is within the range of those reported for relatively lowbinder content WC±Co hardmetals [11±14,31]. This allows us to speculate the above fatigue mechanics analysis, including account of mean stress e€ects, to be suitable for every technical WC±Co hardmetal under relatively generic cyclic loading conditions. 4. Conclusions

Fig. 7. SEM micrograph of a subsurface pore discerned as the failure origin of a sample subjected to cyclic loading.

description of fatigue failure loci according to Goodman's equation is given in this case from the postulation that constant fatigue life is obtained for any combination of alternating and mean stress that lies on a straight line connecting the fully reversed stress for a given life …R ˆ 1† to the rupture stress under monotonic loading …R ˆ 1†. Hence, a failure locus for a runout cycle of 107 may be expressed by

A systematic study comprising experimental characterization and LEFM analysis has been carried out to investigate the fatigue behavior of a ®ne-grained WC±10 wt% Co hardmetal. The main results and conclusions are summarized as follows: 1. The fatigue behavior of the cemented carbide studied may be rationalized on the basis of LEFM, under in®nite fatigue life conditions, by considering initiation of subcritical crack growth as the controlling stage in the fatigue failure phenomena, i.e., FCG threshold as the e€ective toughness under cyclic loading. 2. Within the above fatigue mechanics analysis, the fundamental LEFM correlation among defect size, strength and FCG threshold for large cracks allows to estimate fatigue limit values, under di€erent nonzero mean cyclic stresses, within 10% error relative

Y. Torres et al. / International Journal of Refractory Metals & Hard Materials 19 (2001) 341±348

to those experimentally determined following a staircase procedure. The corresponding fatigue limit predictions are made on the assumption that similitude on fatigue threshold behavior of large and small cracks applies for the cemented carbide investigated. This hypothesis is sustained on the relatively ®ne scale of the microstructure of cemented carbides as compared to typical dimensions of their intrinsic natural ¯aws. 3. FCG rates for the hardmetal studied are found to exhibit an extremely high dependence on the applied stress intensity as well as signi®cant load ratio e€ects. The cyclic crack propagation behavior is signi®cantly dominated by the applied Kmax , an experimental fact related to predominance of static modes of fracture during subcritical FCG. This is suggested to occur as a consequence of the e€ective low ductility intrinsic to the metallic binder resulting from the severe deformation constraints imposed on it by the surrounding hard WC particles. 4. Mean stress e€ects on the fatigue limit of hardmetals may be accounted by a Goodman-like relationship whose slope corresponds to the fatigue sensitivity under zero mean cyclic stress conditions for the material under consideration.

Acknowledgements This work has been funded by the Spanish Comisi on Interministerial de Ciencia y Tecnologia (CICYT) under grants no. MAT1997-0923 and MAT2000-1014-CO201. The authors wish to express their gratitude to DURIT Iberica for providing the material used in this work. They are also grateful to M. Marsal for her SEM assistance as well as to S. Rodriguez for her collaboration in the FCG experiences. One of the authors (Y.T.) would like to acknowledge the scholarship received from the Instituto de Cooperaci on Iberoamericana (ICI).

References [1] Kenny PA. The application of fracture mechanics to cemented carbides. Powder Metall 1971;14:22±38. [2] Chermant JL, Deschanvres A, Iost A. Tenacite de WC±Co 15%. Mater Res Bull 1973;8:925±34. [3] Exner HE, Walter A, Pabst R. Zur ermittlung und darstellung der fehlerverteilungen von spr oden werksto€en. Mater Sci Eng 1974;16:231±8. [4] Lueth RC. Determination of fracture toughness parameters for WC±Co alloys. In: Bradt RC, Hasselmann DP, Lange FF, editors. Fracture mechanics of ceramics. New York: Plenum Press; 1974. p. 791±806. [5] Ingelstr om N, Nordberg H. The fracture toughness of cemented carbide. Eng Fract Mech 1974;6:597±607.

347

[6] Almond EA, Roebuck B. Fatigue-crack growth in WC±Co hardmetals. Metal Technol 1980;2:83±5. [7] Fry PR, Garrett GG. The inter-relation of microstructure, toughness and fatigue crack growth in WC±Co hardmetals. In: Comins NP, Clark JB, editors. Proceedings of the International Conference on Speciality Steels and Hard Materials. London: Pergamon; 1983. p. 375±81. [8] Knee, N, Plumbridge, WJ. The in¯uence of microstructure and stress ratio on fatigue crack growth in WC±Co hardmetals. In: Valluri SR, Taplin DMR, Ramarao P, Knott JF, Dubey R, editors. Proceedings of the 6th International Conference on Fracture. vol. 4, New Delhi; 1984. p. 2685±92. [9] Hirose Y, Boo M-H, Matsuoka H, Park Y-C. In¯uence of stress ratio and WC grain size on fatigue crack growth characteristics of WC±Co cemented carbides. J Soc Mater Sci Jpn 1997; 46:1402±9. [10] Ishihara S, Goshima T, Yoshimoto T, Sabu T. On fatigue lifetimes and crack growth behavior of cemented carbides. In: Wu, XR, Wang, ZG, editors. Fatigue'99, Proceedings of the 7th International Fatigue Congress. vol. 3. Beijing: HEP/EMAS; 1999. p. 1811±6. [11] Schleinkofer U, Sockel HG, Schlund P, G orting K, Heinrich W. Behaviour of hard metals and cermets under cyclic mechanical loads. Mater Sci Eng A 1995;194:1±8. [12] Schleinkofer U, Sockel HG, G orting K, Heinrich W. Microstructural processes during subcritical crack growth in hard metals and cermets under cyclic loads. Mater Sci Eng A 1996; 209:103±10. [13] Schleinkofer U, Sockel HG, G orting K, Heinrich W. Fatigue of hard metals and cermets. Mater Sci Eng A 1996;209:313±7. [14] Schleinkofer U, Sockel HG, G orting K, Heinrich W. Fatigue of hard metals and cermets ± new results and a better understanding. Int J Refract Met Hard Mater 1997;15:103±12. [15] Collins JA. In: Failure of materials in mechanical design. New York: Wiley; 1981. p. 369±74. [16] Torres Y, Casellas D, Anglada M, Llanes L. Fracture toughness evaluation of hardmetals: in¯uence of testing procedure. Int J Refract Met Hard Mater 2001;19:27±34. [17] Tada H, Paris PC, Irwin GR. In: The stress analysis of cracks handbook. St. Louis: Paris Productions Incorporated (and Del Research Corporation); 1973. p. 2.13±5. [18] Almond EA. Deformation characteristics and mechanical properties of hardmetals. In: Viswanadham RK, Rowcli€e DJ, Gurland J, editors. Proceedings of the Internat®onal Conference on the Science of Hard Materials. New York: Plenum Press; 1981. p. 517±61. [19] Llanes L, Torres Y, Casas B, Casellas D, Marimon F, Roure F, Anglada M. Fracture behavior of cemented carbides: a fracture mechanics analysis. In: Proceedings of the 13th European Conference on Fracture, Fracture Mechanics: Applications and Challenges. San Sebastian: Elsevier; 2000. ECF 13 on CDROM. [20] Sigl LS, Exner HE. Experimental study of the mechanics of fracture in WC±Co alloys. Metall Trans A 1987;18:1299±308. [21] Liu S-Y, Chen I-W. Fatigue of yttria-stabilized zirconia: II, crack propagation, fatigue striations, and short-crack behavior. J Am Ceram Soc 1991;74:1206±16. [22] Dauskardt RH, James MR, Porter JR, Ritchie RO. Cyclic fatigue-crack growth in a SiC-whisker-reinforced alumina ceramic composite: long and small-crack growth. J Am Ceram Soc 1992;75:759±71. [23] Badrinarayanan K, McKelvey AL, Venkateswara Rao KT, Ritchie RO. Fracture and fatigue-crack growth behavior in ductile-phase toughened molybdenum disilicide: e€ects of niobium wire vs particulate reinforcements. Metall Mater Trans A 1996;27:3781±92.

348

Y. Torres et al. / International Journal of Refractory Metals & Hard Materials 19 (2001) 341±348

[24] Vasel CH, Krawitz AD, Drake EF, Kenik EA. Binder deformation in WC±(Co, Ni) cemented carbide composites. Metall Trans A 1985;16:2309±17. [25] Ritchie RO, Knott JF. Mechanisms of fatigue crack growth in low alloy steel. Acta Metall 1973;21:639±48. [26] Soboyejo WO, Ye F, Chen L-C, Bahtishi N, Schawrtz DS, Lederich RJ. E€ects of reinforcement morphology on the fatigue and fracture behavior of MoSi2/Nb composites. Acta Mater 1996;44:2027±41. [27] Zinsser Jr. WA, Lewandowski JJ. E€ects of R-ratio on the fatigue crack growth of Nb±Si (ss) and Nb±10Si in situ composites. Metall Trans A 1998;29:1749±57.

[28] Ritchie RO, Gilbert CJ, McNaney JM. Mechanics and mechanisms of fatigue damage and crack growth in advanced materials. Int J Solids Struct 2000;37:311±29. [29] Ritchie RO. Mechanisms of fatigue crack propagation in metals, ceramics and composites: role of crack tip shielding. Mater Sci Eng A 1988;103:15±28. [30] Sigl LS, Fischmeister HF. On the fracture toughness of cemented carbides. Acta Metall 1988;36:887±97. [31] Otsuka A, Tohgo K, Sugawara H, Ueda F. Tension±compression fatigue of WC±12%Co hardmetal. J Soc Mater Sci Jpn 1987; 36:135±40.