Deformation and fracture of WC grains and grain boundaries in a WC-Co hardmetal during microcantilever bending tests

Journal Pre-proof Deformation and fracture of WC grains and grain boundaries in a WC-Co hardmetal during microcantilever bending tests

Tamás Csanádi, Marek Vojtko, Ján Dusza PII:

S0263-4368(19)30534-7

DOI:

https://doi.org/10.1016/j.ijrmhm.2019.105163

Reference:

RMHM 105163

To appear in:

International Journal of Refractory Metals and Hard Materials

Received date:

4 July 2019

Revised date:

20 November 2019

Accepted date:

25 November 2019

Please cite this article as: T. Csanádi, M. Vojtko and J. Dusza, Deformation and fracture of WC grains and grain boundaries in a WC-Co hardmetal during microcantilever bending tests, International Journal of Refractory Metals and Hard Materials(2019), https://doi.org/10.1016/j.ijrmhm.2019.105163

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© 2019 Published by Elsevier.

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Deformation and fracture of WC grains and grain boundaries in a WC-Co hardmetal during microcantilever bending tests Tamás Csanádia,*, Marek Vojtkoa, Ján Duszaa,b a

Institute of Materials Research, Slovak Academy of Sciences, Watsonova 47, 04353 Košice, Slovak Republic

Donát Bánki Faculty of Mechanical and Safety Engineering, Óbuda University, Népszínház utca

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b

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8, 1081 Budapest, Hungary

*

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Corresponding author. Tel: +421-55-7922-412.

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E-mail address: [email protected] (T. Csanádi).

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Abstract

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The deformation and fracture behaviour of constituents of a WC-Co hardmetal were investigated by microcantilever bending technique. The compositions of FIB fabricated

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microcantilevers were: I) single grains of WC, II) WC grains of different orientations and III) the mixture of WC grains and Co phase. The crystallographic orientation of WC grains and the

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fracture surface of beams were studied by EBSD and SEM analyses, respectively. It was revealed that the elastic deformation depends mainly on the composition of the beams and the orientation of the WC grains. The Young’s modulus of WC grains showed an orientation dependence with decreasing values from the basal (E~800 GPa) towards the prismatic orientations (E~500 GPa), which is in agreement with the theoretical predictions. The deformation behaviour of WC grains exhibited plasticity before their fracture with an average fracture strength of σ=12.3±3.8 GPa. It was found that the effect of dislocations and nanometre-sized defects (e.g. pores) plays an important role in the bending test of WC grains. Most of the WC/WC boundaries showed brittle failure with an average fracture strength of σ=4.1±2.5 GPa. It was concluded that the majority of the boundaries in the WC-Co composite are high energy WC/WC boundaries and their fracture strength is generally much lower than that of the WC grains. 1

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Keywords: Fracture strength; grain boundary fracture; elastic anisotropy; microcantilever bending; tungsten carbide-cobalt.

1. Introduction

Tungsten carbide-cobalt (WC-Co) is the most commonly available cemented carbide, or hardmetal, which is widely used for highly demanding applications, such as cutting, forming,

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machining tools, due to its high hardness, good fracture toughness and excellent wear resistance.

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The outstanding properties of WC-Co is strongly related to the complex composite structure of interpenetrating network of the hard WC phase and a tough Co binder. It was found that the main

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role of tungsten carbide in the microstructure is to provide high hardness and wear resistance,

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while the cobalt phase accounts for the global fracture toughness of the composite [1,2]. Improving the mechanical performance of WC-Co designed for specific engineering applications

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requires the understanding of the deformation behaviour of its constituents, which has been extensively studied by various micro- and nanomechanical testing methods [3-15]. Since tungsten

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carbide forms the major phase in the WC-Co, it is believed that its deformation behaviour has the most important effect on macromechanical performance under various compressive forces.

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Tungsten carbide has a hexagonal lattice structure (type P-6m2), with lattice parameters of a= 0.2906 nm and c= 0.2837 nm, built from alternative hexagonal closed packed layers of tungsten

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and carbon atoms [16]. Micro- and nanomechanical testing studies revealed significant anisotropic deformation of WC grains [6,8,11-14] which plays an important role in the development of new-texture WC-Co composites, resulting in increased hardness in cross-sections containing higher fraction of basal WC planes [17]. Macro deformation of low Co content WC-Co is thought to be transmitted through a hard WC skeleton due to its interconnected structure. The process is controlled by the grain boundary sliding and orientation dependent plasticity of the WC grains [11,18,19], but the deformability of the composite is strongly limited by the microstructure and initial defect structure of the constituents. Processing flaws (e.g. pores) and other obstacles in the material (e.g. grain boundaries) that hinder the movement of dislocation and limit the transmission of plastic deformation can act as stress raisers under tensile stresses, initiating cracks and leading to 2

Journal Pre-proof fracture [20]. In order to improve the macro toughness of WC-Co, which is a key parameter for their reliable operation, it is important to understand the mechanical response of its constituents and the role of WC/WC and WC/Co boundaries. Since the above mentioned defects significant affect the fracture properties, direct micromechanical investigations are needed to determine the fracture behaviour of the constituents of the WC-Co composites, instead of estimates from single crystals of WC and Co. To the best of our knowledge, only a few papers have studied the fracture behaviour of WC-Co under tensile stress condition at the level of grains, applying directly microtension [10,20] and microcantilever bending tests [5,9,15]. In these works, the fracture strength of

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WC grains [9,15], WC/WC boundaries [5,10,15] and WC/Co interfaces [10] was determined based on experimental load-displacement data using analytical and FEM methods. For individual

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WC grains, the fracture strength was estimated to be 6-7 GPa by Trueba et al. [9], while

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significantly higher values of 19.5-25.3 GPa were found by Elizalde et al. [15]. Regarding the WC/WC boundaries, fracture strengths range from ~3 GPa up to ~25 GPa [5,10,15], where high

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values above ~19 GPa are attributed to strong highly coherent, so-called coincidence site lattice

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(Σ=2) twist (CSL2), boundaries [15]. It is important to note that the latter high strength of the WC/WC boundaries was only considered as an estimate of the lower bound because they were found to be at least as strong as the WC grains [15].

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In order to understand the fracture properties of the WC-Co constituents and to explain the scatter of the measured fracture strength values reported for both WC grains and WC/WC

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boundaries, a systematic microcantilever bending study was carried out. The aim of this work is

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to investigate the deformation and fracture behaviour of WC grains, WC/WC and WC/Co boundaries and to determine the main factors that have influence on cracking caused by tensile stresses.

2. Material and experimental methods

The tungsten carbide-cobalt composite used in the present work was a coal-mining-grade sample supplied by a member company of the British Hardmetal Association. It was prepared by pressureless sintering with a Co volume fraction of 16.7%. The sample was subjected to standard metallographic procedures, including cutting, grinding and polishing on a Struers machine. The final polishing was carried out on a velvet polishing disc using a polycrystalline diamond 3

Journal Pre-proof suspension (crystal size of 0.1 μm). To prepare the surface for electron backscatter diffraction (EBSD) analysis, a further high precision ion-milling was required, performed by a SEMPrep machine using Ar ions. For the preparation of microcantilevers, the polished sample was investigated by scanning electron microscopy (SEM) and EBSD on a FEI Quanta 3D machine. The crystal orientation of the WC and Co grains/phases was determined from the measured EBSD maps using Orientation Imaging (OIM) software (EDAX). The program describes the orientation of the crystals based on Euler angles (φ1,Φ,φ2) relative to the sample coordinate system. Further details on sample preparation and EBSD analysis can be found in our earlier

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work [11].

Microcantilevers were fabricated by a focused ion beam (FIB) technique in a dual-beam

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FIB/SEM Zeiss Auriga microscope operated at 30 kV. Milling was carried out in three

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consecutive steps, which included the preparation of trenches, cutting and final polishing of the micocantilevers with the corresponding currents of 20 nA, 2 nA and 500 pA, respectively [21].

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Based on previous EBSD maps, fifteen microcantilever beams were fabricated in WC-Co in three

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different types of location: I) which were completely located in a single WC grain (6 pieces), II) consisted of WC grains of different orientations (6 pieces) and III) it contained Co phase between the WC grains (3 pieces). In the latter case, the beams were prepared so that the Co phase is

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located near the fixed end of the cantilever (closer than half the length of beam). The beams were fabricated with the geometry of pentagonal cross-sections, with prepared lengths of L=11.1-23.5

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μm, widths of a=3.1-4.0 μm and total thicknesses of b+ma=2.7-4.1 measured by SEM as shown

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schematically in Fig. 1. The size of the beams depended on the size and shape of the grains at the location where they were fabricated. The geometry and composition of the FIB milled microcantilevers are listed in Tab. 1. The bending test of the microcantilevers was carried out on an Agilent G200 NanoIndenter equipped with a diamond spherical tip with a nominal radius of 1 micron, using a constant load rate of 0.016 mN/s. Based on preliminary tests, the maximum load was set to 8 mN, which was high enough to induce fracture in the microcantilevers. The loading process was carefully monitored and was immediately interrupted manually after the fracture occurred (before reaching the maximum load) and then the testing process was followed by the unloading. As a result, broken cantilevers were formed, which in some cases remained in one piece. Bending tests were started after reaching a predefined drift limit of 0.1 nm/s and each test was corrected for the drift 4

Journal Pre-proof rate measured at the end of the process, which was similar to the predefined limit. The measured load-displacement data were corrected for the slight penetration depth caused by the indentation that accompanies the bending test, similar to that as reported in [22]. After bending tests, SEM was used to analyze the broken microcantilevers and fracture surfaces of each specimen. The dimensions of the beams and the fracture distance (x1) in Fig. 1 were determined based on SEM micrographs. Using appropriate microscope to indenter calibration on Agilent G200, the loading point (x2) was measured based on the position of the cross-hair relative to the free end of the beam according to an optical micrograph of 2500x magnification acquired prior to each test. The

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accuracy of tip positioning was about 0.2 μm as confirmed by further SEM analysis on beams,

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3. Background to the analysis of bending tests

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which remained in one piece after testing and showed a slight impression at the loading point.

The microcantilever bending tests were evaluated according to Euler-Bernoulli beam

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theory, which is only valid for small deflections. The fabricated microcantilevers were considered to be homogeneous and were loaded by an F force at their free end (volume forces are

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negligible). During bending, this resulted in tensile and compressive deformation in the upper and lower layers of the beam, respectively. It is assumed that there is a neutral surface along the

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beam, whose length does not change during bending, and any cross-sectional plane remains

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perpendicular to that after the deflection [23]. The length of the beams (L), the fracture distance (x1) and the loading position (x2) from the ends, as well as the geometric parameters of pentagonal cross-section (a, ma, b) are indicated in Fig. 1. The origin of the Cartesian coordinate system (X, Y, Z) is attached to the fixed end of the cantilevers, where the rectangular and triangular parts of the cross-section are connected (see Fig. 1). The distance between the neutral plane and the X-Y plane is denoted by z0. The position of the neutral axis, which coincides with the centre of gravity of the beam, was calculated to as follows (see Appendix): 𝑧0 =

1

𝑚 𝑏+ 𝑎 2

𝑏2

(2 −

2 𝑚𝑎

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)

(1)

Using the above notations, the stress (𝜎𝑥𝑥 ), strain (𝜀𝑥𝑥 ) and deflection (u) of any cross-sectional point of the cantilevers along the X-axis are derived from the beam theory [23]: 5

Journal Pre-proof 𝜎𝑥𝑥 = 𝜀𝑥𝑥 =

𝐹(𝑧−𝑧0 ) 𝐼𝑥 𝐹(𝑧−𝑧0 ) 𝐸𝐼𝑥

(𝐿 − 𝑥2 − 𝑥)

(2)

(𝐿 − 𝑥2 − 𝑥)

(3)

𝐹

𝑥

𝑢 = − 2𝐸𝐼 𝑥 2 (𝐿 − 𝑥2 − 3)

(4)

𝑥

where E represents the Young’s modulus of the beam in the X-axis and Ix denotes the second moment of area of the beam’s cross-section. For the pentagonal shape shown above, Ix is obtained as follows (see Appendix): 3

+

3 𝑎𝑚𝑎

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− 𝑎 (𝑏 +

𝑚𝑎

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𝑎𝑏 3

2

) 𝑧02

(5)

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𝐼𝑥 =

Figure 1: Schematic of an as-fabricated microcantilever with a pentagonal cross-section, which fractures at x=x1 due to the applied load of F at a distance of x2 from its free end. Within the limitations of beam theory, the applied load (F) and vertical displacement of the loaded point (h) at the position of x=L ̶ x2 are in a linear relationship, and the Young’s modulus can be calculated according to Eq. (4).

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Journal Pre-proof 𝐹

𝐸 = 3ℎ𝐼 (𝐿 − 𝑥2 )3

(6)

𝑥

Since fracture may occur at x=x1 for some reasons (e.g. weak grain boundary), the highest tensile stress that probably initiated the fracture at this cross-section is located on the top surface of the beam (z=b). The corresponding stress value is considered to be the fracture strength (𝜎) of the beam according to Eq. (2). 𝜎=

𝐹(𝑏−𝑧0 ) 𝐼𝑥

(𝐿 − 𝑥2 − 𝑥1 )

(7)

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The Young’s modulus and fracture strength of microcantilevers were determined according to Eqs. (6) and (7). Within the frame of theory of linear elasticity, the deformation of

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microcantilevers at the location of fracture on the top of the beams was derived from Eqs. (6) and (7) as follows:

3ℎ(𝑏−𝑧0 )(𝐿−𝑥2 −𝑥1 ) (𝐿−𝑥2 )3

(8)

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𝜎

𝜀=𝐸=

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4. Results of microcantilever bending tests

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The tested WC-Co composite had an average grain size of 8.93±0.72 μm with a volume fraction of cobalt of 16.7% as determined by image analysis software (Image J) based on the

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characteristic microstructure of the EBSD image illustrated in Figs. 2a. According to the EBSD image, the grains appeared to be randomly oriented and covered a wide range of crystal

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orientations. The corresponding inverse pole figure legend of the WC grains and the schematic representation of the crystal orientation relative to the sample coordinate system are shown in Fig. 2c. The outline of the beams is shown schematically on the EBSD map while the corresponding as-prepared microcantilevers are shown in the SEM image. In Figs. 2a,b, all the three types of FIB milled microcantilevers are visible: I) single grain of WC (beams A, I, J), II) WC grains of different orientations (beams G, K), III) different WC grains and Co phase (beam H). A typical as-prepared microcantilever with a pentagonal cross-section is shown in Fig. 2d. Microcantilevers in WC grains were FIB milled intentionally so that the beams were orientated approximately perpendicular to the neutral line (green line in Fig. 2c) of a selected grain, which resulted in φ1≈0 as shown in Fig. 2a. In other words, the beam axis (x) lies in the plane of the tilt (Zc-Zs plane) in Fig. 2c. This method simplified the evaluation of the beam orientation, which 7

Journal Pre-proof was characterized only by the tilt (Φ) and rotation (φ2) angles. Here, Φ is the angle of rotation of the crystal from the basal (0001) orientation and φ2 denotes the angle from one type of prismatic type (101̅0) to the other type (21̅1̅0) . The exact geometry and composition of each microcantilever prepared, including the crystal orientation of each single WC, are listed in Tab.

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1.

Figure 2: The microstructure of the WC-Co composite tested: a) EBSD image with the outline of beams, b) SEM image with the as-prepared microcantilevers. c) Inverse pole figure legend of the WC grains corresponding to the EBSD map and schematic representation of the crystal orientation relative to the sample coordinate system [11]. d) Inclined view of a typical microcantilever with a pentagonal shape cross-section.

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Journal Pre-proof The bending tests revealed that the majority of microcantilevers were fractured in WC grains (8 cases) or at the WC/WC boundaries (5 cases) regardless of the beam composition (see Tab. 1). The fracture was connected to the presence of Co phase in only two cases. Based on this, microcantilevers were classified into two main groups according to the mode of failure: 1) fracture in the WC grains and 2) fracture at the WC/WC (or WC/Co) boundaries. Deformation behaviour and fracture surfaces of the respective failure modes are shown in Fig. 3 and Fig. 4, respectively. In order to eliminate the influence of the size of microcantilevers and to represent the deformation by an intensive parameter, the stress-strain curves were calculated at the fracture

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site on the top of the beams according to Eqs. (7), (8). These curves are plotted instead of the measured load-displacement data in Figs. 3a and 4a. We are aware that the stress-strain curves

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are valid only for the elastic region, but regarding that that the deviation from elasticity is small,

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this provides a good analytical approximation of the stress-strain behaviour of the beams. Regarding the fracture mode 1), the load-displacement curves of the beams fractured in the

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WC grains, without exception, exhibit a deflection from the linearity before their final failure. This is visible on the stress-strain curves in Fig. 3a. Six microcantilevers fractured practically at

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their fixing (within a distance of 1 μm) and only two were broken at a distance of 2-3 microns from the fixing. In this work, the term fixing refers to the place where the beams are connected to

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the support material as shown in Fig. 3b and Fig. 4b. Taking into account that the tensile stress is maximal on the top of the beams at the fixing according to Eq. (2), the above mentioned six

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cantilevers were considered ‘defect free’ while the remaining two were considered ‘defected’ as

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listed in Tab. 1 and shown schematically in Fig. 3b. Here, it is important to note that based on finite element analysis (FEM) the maximal tensile stress on the top surface of beams is not exactly at the fixing but slightly displaced therefrom (~5% of the beam length), depending on geometry and material properties [5,9]. In our case, this predicts a displacement of about 1 micron, even for the longest microcantilever, where the fracture occurs practically at the fixing. Regarding the SEM images of broken cantilevers, which exhibit microcracks and slip lines in some cases (see beams A and C, respectively), there is evidence for plasticity before the final failure of the WC grains during bending test. This plastic property can be seen on the calculated stress-strain graphs, whether it is ‘defect free’ or ‘defected’. Additionally, the yield point of each beam is clearly discernible in Fig. 3a, similar to that was reported for WC grains during mircocantilever bending earlier [9]. The present results support that WC grains are not inherently 9

Journal Pre-proof brittle but can undergo limited plastic deformation even in tension similar to that reported during indentation [6,11,19], micro-compression [8,24] and nanoscatch testing [12,25]. The analysis of stress-strain curves in terms of fracture strength and Young’s modulus of the microcantilevers is discussed in the Discussion part. As for the SEM micrographs in Figs. 3c-i, the fracture surfaces exhibit various irregular shapes, which are presumably connected to the anisotropy of crystal structure, slip activation and cleavage strengths [26-28]. Although the presumed fracture origins were carefully analyzed by SEM, defect points were clearly identified only for the two ‘defected’ beams in the form of nanometre-sized pores as shown for beam D in Fig. 3i. The defect points of

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‘defect free’ beams were hardly discernible even at 100.000x magnification. Considering the plastic properties of the stress-strain curves in Fig. 3, crack initiation is presumably related to the

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interaction of dislocations (see Figs. 3c,h) and their accumulation at specific locations (see for

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beams A and C in Figs. 3c,e,f,h) rather than the presence of nanometre-sized pores.

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Figure 3: Fracture of microcantilevers in WC grains: a) stress-strain curves corresponding to the upper surface of the beams at the facture site calculated from the measured loaddisplacement data, b) schematic of the fracture origins in the WC grains, c)-e) top and f)-i) inclined view SEM images of the fracture surfaces.

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Figure 4: Fracture of microcantilevers at the boundary of WC grains: a) stress-strain curves corresponding to the upper surface of the beams at the fracture site calculated from the measured load-displacement data, b) schematic of fracture origins at the WC boundaries, c) outline of a beam FIB milled from two WC grains with d) the corresponding top view SEM image of the broken surface. e)-g) Inclined view SEM images of the different fracture surfaces. 12

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Concerning the mode of failure 2), it was found that the dominant fracture mode associated with WC boundaries is related to the ‘WC/WC boundary’ rather than the ‘WC/Co boundary’ although both are possible as illustrated in Fig. 4b. The fracture sites were found at the WC/WC boundaries as indicated in Tab. 1. Fracture was also observed at the WC/WC boundary even in a beam (beam N) which contained a small amount of Co only on its upper surface closer to the fixing than the WC/WC boundary (see Tab. 1). Contrary to WC grains, the majority of microcantilevers that fractured at WC/WC boundaries exhibited brittle fracture similar to that as

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is known at macro scale WC-Co specimens [5], as shown in Fig. 4. The corresponding loaddisplacement and stress-strain curves show a linear relationship and the fracture surfaces are

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smooth (see Fig. 4f). This suggests that plasticity is not probable in this case. The beams fracture

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right after the linear elastic deformation due to the presence of weak WC/WC boundaries close to the fixing (see curves for beams F and G in Fig. 4a). The cracks start at the WC/WC boundaries,

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leading to a sudden fracture across the grain boundaries as shown for beam F in Figs. 4c,d,f.

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These results differ from that reported for WC/WC CSL2 boundaries [15], where the fracture was intragranular, indicating that the WC/WC CSL2 interface is as strong as a WC grain. In agreement with the results reported in [15], the present study suggests that the deformation

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characteristic of WC/WC boundaries strongly depends on the relative orientation of adjacent grains, which is described in more detail in the Discussion part along with the corresponding

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fracture strength values. In addition to the brittle failure of the WC/WC boundaries, slight

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plasticity was also observed in some cases as shown for beam E in Figs. 4a,e. This is due to the inclined orientation of the grain boundary, which is not perpendicular to the beam axis. Consequently, in a loaded beam, the stresses are slightly different on the two sides of the upper surface of the inclined WC/WC boundary and cracking is initiated at the side first that is closer to the fixing (where the stress is higher). Then, due to the presence of a crack on one side, the increased stress on other side of the beam at that cross-section leads to tearing or fracture of a small fragment of the WC grain while the crack propagates across the WC/WC boundary (see Fig. 4e). Therefore, fracture is not as sudden as in the case of a perpendicular boundary and it can be recorded as a slight deviation from the linearity on the load-displacement data as shown for beam E in Fig. 4a. Regarding the cantilevers that fractured at the WC/Co boundary, a more significant plasticity was found than that which was observed even in WC grains. The extent of 13

Journal Pre-proof plastic deformation was lager in beams with higher Co phase content. This is visible in the case of beam H, which consists of two WC grains separated by a Co phase, as shown in Fig. 2. In this beam, it is assumed that the softer and more ductile Co phase begins to deform plastically first, earlier than the WC grains, resulting in a continuous deviation from linear load-displacement or stress-strain curve (see Fig. 4a). The increasing load initiates cracking both in the Co and at the WC/Co boundary, which does not lead to a catastrophic failure, but subsequently, a significant fracture occurs in WC as shown in Fig. 4g.

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5. Discussion

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5.1 Elastic properties of constituents of a WC-Co composite

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The elastic behaviour of microcantilevers was characterized by their Young’s modulus in the direction of the beam axis, which was determined according to Eq. (6) and listed in Tab.1.

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The results obtained were correlated to the elastic anisotropy of the WC grains, the influence of

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WC multigrain structures and the presence of the Co phase. Young’s modulus was calculated for each beam tested, regadless of composition. Here, it is important to emphasize that the effect of a slight penetration of the indenter tip into the beam the during bending test was corrected for the

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load-displacement curve of the indentation of the WC grains [22]. The Young’s modulus of each beam was evaluated from the linear part of the experimental data shown in Fig. 3a and Fig. 4a.

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The obtained E values exhibited a large scatter in the range of ~300-800 GPa (see Tab. 1).

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Analysis of Young’s modulus values revealed that the scatter is attributed to two main factors, which are the crystal orientation of WC grains and the composition of the beams, as illustrated in Fig. 5.

To study the effect of crystal orientation on the Young’s modulus, the microcantilevers were analyzed using SEM images recorded during FIB milling and taken after their fracture. Based on this process, only six specimens were found that were located entirely in the WC grains. Their orientation was characterized by the Φ tilt angle as listed in Tab. 1, which measures the crystal rotation from the basal towards the prismatic orientations. The Euler angles φ1 and φ2 are irrelevant, since φ1≈0 and the rotation of φ2 has no influence on the elastic properties due to the transversely isotropic symmetry of hexagonal WC. The orientation dependence of the Young’s modulus of WC grains, which exhibits a significant decrease with increasing Φ, is 14

Journal Pre-proof plotted in Fig. 5a. Here, in Fig. 5, it is important to note that Φ denotes the tilt angle from the basal orientation of the WC crystal relative to the direction of tension/compression (X axis in Fig. 1) and not relative to the normal of the sample surface. To understand the tendency in experimental data, the Young’s modulus of WC grains were predicted based on the elastic constants of WC monocrystals [29] according to the equation reported for hexagonal grains of ZrB2 in our earlier work [30] as follows: 𝐸 = (𝑠11 ∙ 𝑠𝑖𝑛4 Φ + (2 ∙ 𝑠13 + 𝑠44 ) ∙ 𝑠𝑖𝑛2 Φ ∙ 𝑐𝑜𝑠 2 Φ + 𝑠33 ∙ 𝑐𝑜𝑠 4 Φ)−1

(8)

−1

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where the s11, s13, s33 and s44 are the components of 𝑆𝑖𝑗 = (𝐶𝑖𝑗 ) compliance tensor derived from the elastic constants (see Appendix), which are c11=720 GPa, c12=254 GPa, c13=267 GPa, c33=972

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GPa and c44=328 GPa in the coordinate system where x3 is parallel with the axis of the hexagonal

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[29]. The theoretical model and experimental data exhibit similar orientation dependence, with better agreement for near basal orientation (Φ=0°) than for prismatic (Φ=90°), where the

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corresponding experimental values are 800 GPa and 500 GPa, respectively. This confirms that the Young’s modulus of WC grains is much higher along the axis of symmetry (c-axis) than

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perpendicular to the c-axis. It is important to note that both the measurement error of the beam dimensions and the deviation of the as-fabricated microcantilevers from the ideal geometry used

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in the beam theory influence the evaluation of the Young’s modulus. The latter can be taken into account using FEM simulations as reported in [9]. However, the present work has shown that the

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proposed approach, using microcantilever bending experiments in combination with the theory of

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linear elasticity, is a useful tool for approximating Young’s modulus of grains of anisotropic materials such as WC.

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Figure 5: a) Orientation dependence of Young’s modulus of WC grains measured by microcantilever bending tests and estimated from single crystal elastic constants [29]. b) The influence of beam composition on the Young’s modulus of microcantilevers in the tested WC-Co composite. 16

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Regarding the effect of beam composition on the Young’s modulus, the experimental data for all measurements are plotted in Fig. 5b. The results were grouped according to the beam composition as ‘single grain of WC’, ‘multiple grains of WC’ and ‘WC grains with Co phase’, where the first group (black dots) is identical to that plotted in Fig. 5a. In addition to the experimental data, the variation of the Young’s modulus of WC and Co phases caused by their anisotropic nature is also indicated [29,31]. Figure 5b shows that the presence of Co phase significantly reduces E to 300 GPa (see blue triangles) and the decrease depends on the volume

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fraction of Co. Considering the Young’s modulus of multiple WC grains (red squares), the graph shows a large scatter with a lowest value of nearly 300 GPa. This suggests that some of the

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WC/WC boundaries are very compliant and/or may contain a Co phase as well, resulting in a

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much lower Young’s modulus for the WC grains than the corresponding theoretical value. Additionally, it is important to note that the determination of Young’s modulus of the composite

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structure is only approximate since the theory of linear elasticity applies only to homogenous

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materials. Any deviation from the homogenous structure should be carefully investigated using the FEM method, which is beyond the scope of this work.

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5.2 Fracture strength of WC grains and WC/WC boundaries

ur

The fracture strength of the microcantilevers tested was evaluated according to Eq. (7),

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which is listed in Tab. 1 and plotted in Fig. 6. The results were divided into three groups according to the location of the fracture: 1) in WC grains (8 cases), 2) at the WC/WC boundaries (5 cases) and 3) at the WC/Co boundaries (2 cases). It is important to note that the fracture strength values do not overlap the results of Young’s modulus because there is no strict correlation between them. For example, in the case of two multi-grain WC beams, fractures occurred inside the WC grains instead of the WC/WC boundaries. In addition to our present results, the fracture strength values reported in the literature for WC-Co composites [9,10,15] are also plotted in Fig. 6. Regarding the first group measured in the present work, which includes both ‘defect free’ and ‘defected’ fractures in WC, the average fracture strength was found to be σ=12.3±3.8 GPa. The two lowest values (less than 10 GPa) belong to those microcantilevers (beams D and J in 17

Journal Pre-proof Tab. 1) where the defect points were identified. In the case of ‘defect free’ beams, fracture strength is in the range of 11.1 GPa to 20.5 GPa and has no correlation with orientation, unlike the corresponding Young’s modulus values. The crystal orientation is presumably has an influence on the anisotropic slip activation and fracture strength of the WC grains, similar to that reported for Ti [27], but this is negligible compared to the defect structure of the beams. Although the identification of defect points remains a challenge and the mechanisms of cracking are not yet completely understood, it is primarily the interactions of dislocations, their accumulation at a given locations, and the distribution of defects of different sizes (e.g. pores)

of

that play an important role during bending tests of WC grains. Figure 6 shows that the strength of the WC crystals varies over a wide range and can reach such high values that were reported for

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WC grains in [15]. Additionally, our results exhibit a bridge between the high and low strength

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values reported by Trueba et al. [9] and Elizalde et al. [15], respectively. This indicates the strength of WC grains has a wide variation within one sample, which is controlled by the local

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defect structure.

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The average fracture strength of WC/WC boundaries was found to be σ=4.1±2.5 GPa in the present work. Taking into consideration the literature data [10,15], the strength of the WC/WC boundaries exhibits the largest scatter as shown in Fig. 6. Here, it is important to emphasize that

na

fracture strength values of above ~19 GPa are only estimated values since those were found to be at least as strong as the WC grains [15]. In agreement with the conclusions reported by Elizalde

ur

et al. [15], Fig. 6 shows that the relative orientation of adjacent grains is the main factor, which

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controls the fracture strength of WC/WC boundaries. Based on the present work and literature data [10, 15], it is concluded that the majority of WC/WC boundaries in the WC-Co composite are so-called high energy boundaries, in which atoms are highly disordered with a lower coordination number than in the bulk. Therefore, the adjacent grains are loosely connected to each other and thus possess lower fracture strength than that of the WC grains, regardless of the testing method. In specific cases, where some of the atomic sites overlap in adjacent grains in the so-called coincidence site lattice (CSL), low energy, highly coherent boundaries are formed. In WC, the presence of a special (Σ=2) twist CSL2 boundary was predicted [32] and its high strength was confirmed [15], which is comparable to WC grains (see Fig. 6). However, the probability of finding CSL2 in the WC-Co microstructure is low because the majority of WC/WC boundaries are high energy grain boundaries. This was confirmed by the analysis of the 18

Journal Pre-proof misorientation angles done based on the EBSD map in Fig. 2a, revealing that ~80% of the boundaries have an angle of 15°-88° and only 11% fall in the range of 88°-90°. The fracture strength of the WC/Co boundaries, including the presence of WC/WC boundaries and Co phase, is the lowest in Fig. 6. Results are mostly confined to microtensile tests that show strong dependence on the volume fraction of Co [10]. Microcantilever bending experiments on WC/Co boundaries exhibit slightly higher fracture strength compared to microtensile tests, which is attributed to their lower Co content. Finally, considering that the majority of the boundaries in the WC-Co composite are high

of

energy WC/WC boundaries or WC/Co interfaces, it is concluded that the fracture strength of the

Jo

ur

na

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re

-p

ro

WC boundaries is generally much lower than that of the WC grains.

Figure 6: Fracture strength of WC grains, WC/WC and WC/Co boundaries in WC-Co composites measured by microcantilever and microtensile testing [9,10,15]. Note that strength

19

Journal Pre-proof data for low energy WC/WC grain boundaries are estimated values since those were found to be at least as strong as the WC grains [15].

6. Conclusions

The deformation and fracture behaviour of the WC grains, WC/WC and WC/Co boundaries were investigated in a WC-Co composite during microcantilever bending experiments. Regarding the elastic deformation of the beams, it was revealed that the Young’s modulus

of

of the microcantilevers depends strongly on the composition of the beams and the orientation of

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the WC grains. The bending test of microcantilevers FIB milled entirely from single WC grains exhibited an orientation dependent Young’s modulus, which was characterized by the Φ tilt angle

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that measures the crystal rotation from the basal towards the prismatic orientations. It showed a

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decreasing tendency from the basal (Φ=0°) to the prismatic (Φ=90°) orientations with the corresponding values of 800 GPa and 500 GPa, respectively. It was revealed that the orientation

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dependence of the experimental Young’s is consistent with the theoretical prediction, which is based on the single crystal elastic constants of WC. The presence of Co phase and its volume

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fraction in the beams tested could reduce the Young’s modulus to 300 GPa, which is close to the upper limit of the Young’s modulus of the hexagonal Co.

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Considering the fracture behaviour of the beams, it was found that the majority of the microcantilevers fractured in WC grains or at the WC/WC boundaries. The WC grains exhibited

Jo

plasticity with a well-defined yield point before their final failure. This was suggested based on both the measured load-displacement of WC grains and the calculated stress-strain curves, which was confirmed by SEM, showing slip lines close to their fracture surface. The average fracture strength of the WC grains was σ=12.3±3.8 GPa, while the maximum value was measured to 20.5 GPa. The scatter of the measurement is mainly attributed to the interaction of the dislocations that accumulation at a specific location and partly to the nanometre size defects (e.g. pores), which play an important role in bending tests of WC grains. The analysis of the WC/WC boundaries revealed that the deformation and fracture behaviour strongly depends on the relative orientation of the adjacent grains. In most cases, the fracture was brittle without showing plasticity on the load-displacement data (or on the stressstrain curves) and the fracture surfaces were smooth. The average fracture strength of WC/WC 20

Journal Pre-proof boundaries was σ=4.1±2.5 GPa. The present results are consistent with the literature and confirm that the relative orientation of adjacent grains is the main factor, which controls the fracture strength of WC/WC boundaries. Finally it was concluded that the majority of the boundaries in the WC-Co composite are high energy WC/WC boundaries and WC/Co interfaces, and their fracture strength is generally much lower than that of the WC grains.

Acknowledgements

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The authors gratefully acknowledge the financial support of the Slovak Grant Agency for

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Science by the projects: VEGA 2/0163/16, VEGA 2/0091/18, APVV-14-0385, APVV-15-0469 and M-ERA.NET2 (DURACER). This work was realized within the frame of the project

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„Research Centre of Advanced Materials and Technologies for Recent and Future Applications “PROMATECH” ITMS: 26220220186, which was supported by the Operational Program

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“Research and Development” financed through European Regional Development Fund.

Appendix

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Calculation of the second moment of area for the pentagonal cross-section Figure 1 shows the position of the neutral axis (𝑟𝑐 ) in the (Y, Z) coordinate system, which

ur

coincides with the centre of gravity of the beam and was calculated for a pentagonal cross-section

𝑟𝑐 =

Jo

with a thickness of t and density of ρ as follows: 𝑚1 𝑟1 +𝑚2 𝑟2 𝑚1 +𝑚2

=

𝜌𝑡𝐴1 𝑟1 +𝜌𝑡𝐴2 𝑟2 𝜌𝑡𝐴1 +𝜌𝑡𝐴2

=

0 0 𝑎𝑚 ) 𝑎𝑏( ⁄ )+ 𝑎 ( 2 −𝑚𝑎 ⁄3 𝑏 2 𝑎𝑚𝑎 𝑎𝑏+ 2

=

1

𝑚 𝑏+ 𝑎 2

(𝑏2 2

0 −

2) 𝑚𝑎

(A1)

6

where m1 and m2 represents the mass of the rectangular and triangular parts of the cross-section, respectively. The corresponding cross-sectional areas and centre of gravity vectors are 𝐴1 = 𝑎𝑏, 𝐴2 =

𝑎𝑚𝑎 2

and 𝑟1 = (

0 0 ), 𝑟 = ( ), respectively. −𝑚𝑎 ⁄3 𝑏⁄2 2

The second moment of area for the pentagonal cross-section (𝐼𝑥 ) is composed of the second moment of areas of the corresponding rectangular (𝐼1 ) and triangular (𝐼2 ) cross-sections with respect to the neutral axis, which were calculated according to the Parallel axis (Steiner’s) theorem as follows: 21

Journal Pre-proof 𝐼𝑥 = 𝐼1 + 𝐼2 = 𝐼𝑟1 + 𝐴1 𝑑12 + 𝐼𝑟2 + 𝐴2 𝑑22

(A2)

where 𝐼𝑟1 and 𝐼𝑟2 are the second moment of areas with respect to the centre of gravity for the rectangular and triangular parts of the cross-section, which are displaced from the neutral axis by distances of 𝑑1 = |𝑟1 − 𝑟𝑐 | and 𝑑2 = |𝑟2 − 𝑟𝑐 |, respectively. The 𝐼𝑟1 and 𝐼𝑟2 values were obtained according to the below equations. ,

𝑏 − ,− 2 2

𝑧 2 𝑑𝑧𝑑𝑦 =

𝑎 𝑚𝑎 , 3 2𝑚 2𝑚 0,− 𝑎 + 𝑎 𝑥 3 𝑎

(A3)

12

𝑧 2 𝑑𝑧𝑑𝑦 =

3 𝑎𝑚𝑎

36

(A4)

ro

𝐼𝑟2 = 2 ∬2

𝑎𝑏 3

of

𝑎𝑏

𝐼𝑟1 = ∬2𝑎2

Substituting the above equations into Eq. (A2), the second moment of area for the pentagonal

12

+

3 𝑎𝑚𝑎

36

− 𝑎 (𝑏 +

re

𝑎𝑏 3

𝑚𝑎 2

) 𝑧02

(A5)

lP

𝐼𝑥 =

-p

cross-section was obtained to the following simplified form:

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References

173.

ur

[1] H.E. Exner, Physical and chemical nature of cemented carbides, Int Metal Rev 4 (1979) 149-

Jo

[2] B. Roebuck, E.A. Almond, Deformation and fracture processes and the physical metallurgy of WC-Co hardmetals, Int Mater Rev 33 (1988) 90-110. [3] M.G. Gee, B. Roebuck, P. Lindahl, H.O. Andren, Constituent phase nanoindentation of WC/Co and Ti(C,N) hard metals, Mater Sci Eng A 209 (1996) 128–136. [4] N. Cuadrado, D. Casellas, L. Llanes, I. Gonzalez, J. Caro, Effect of crystal anisotropy on the mechanical properties of WC embedded in WC-Co cemented carbides, In Proceedings of the Euro PM2011 Powder Metallurgy Congress & Exhibition (2011) 215–220. [5] T. Klünsner, S. Wurster, P. Supancic, R. Ebner, M. Jenko, J. Glätzle, Effect of specimen size on the tensile strength of WC-Co hard metal, Acta Mater 59 (2011) 4244–4252. [6] B. Roebuck, P. Klose, K.P. Mingard, Hardness of hexagonal tungsten carbide crystals as a function of orientation, Acta Mater 60 (2012) 6131–6143. 22

Journal Pre-proof [7] A. Duszová, R. Halgaš, M. Bľanda, P. Hvizdoš, F. Lofaj, J. Dusza, J. Morgiel, Nanoindentation of WC-Co hardmetals, J Eur Ceram Soc 33 (2013) 2227–2232. [8] T. Csanádi, M. Bľanda, A. Duszová, N.Q. Chinh, P. Szommer, J. Dusza, Deformation characteristics of WC micropillars, J Eur Ceram Soc 43 (2014) 4099-4103. [9] M. Trueba, A Aramburu, N. Rodríguez, I. Iparraguirre, M.R. Elizalde, I. Ocaña, J.M. Sánchez, J.M. Martínez-Esnaola, “In-situ” mechanical characterisation of WC–Co hardmetals using microbeam testing, Int J Refract Met Hard Mater 43 (2014) 236–240. [10] T. Namazu, T. Morikaku, H. Akamine, T. Fujii, K. Kuroda, Y. Takami, Mechanical

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reliability of FIB fabricated WC–Co cemented carbide nanowires evaluated by MEMS tensile testing, Eng Fract Mech 150 (2015) 126–134.

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[11] T. Csanádi, M. Bľanda, N.Q. Chinh, P. Hvizdoš, J. Dusza, Orientation dependent hardness

-p

and nanoindentation induced deformation mechanisms of WC crystals. Acta Mater 83 (2015) 397–407.

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[12] T. Csanádi, M. Novák, A. Duszová-Naughton, J. Dusza, Anisotropic nanoscratch resistance

lP

of WC grains in WC–Co composite, Int J Refract Met Hard Mater 51 (2015) 188–191. [13] J.J. Roa, E. Jimenez-Pique, C Verge, J. Tarragó, A. Mateo, J. Fair, L. Llanes, Intrinsic hardness of constitutive phases in WC-Co composites: Nanoindentation testing, statistical

na

analysis, WC crystal orientation effects and flow stress for the constrained metallic binder, J Eur Ceram Soc 35 (2015) 3419–3425.

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[14] J.J. Roa, P. Sudharshan Phani, W.C. Oliver, L. Llanes, Mapping of mechanical properties at

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microstructural length scale in WC-Co cemented carbides: Assessment of hardness and elastic modulus by means of high speed massive nanoindentation and statistical analysis, Int J Refract Met Hard Mater 75 (2018) 211–217. [15] M.R. Elizalde, I. Ocaña, J. Alkorta, J.M. Sánchez-Moreno, Mechanical strength assessment of single WC-WC interfaces present in WC-Co hardmetals through micro-beam bending experiments, Int J Refract Met Hard Mater 72 (2018) 39–44. [16] S. Lay, C.H. Allibert, M. Christensen, G. Wahnström, Morphology of WC grains in WC-Co alloys, Mat Sci Eng A 486 (2008) 253-261. [17] X. Wang, H. Wang, R. Moscatelli, X. Liu, X. Song, Cemented carbides with highly oriented WC grains and formation mechanisms, Mat Sci Eng A 659 (2016) 76-83.

23

Journal Pre-proof [18] S. Lay, HRTEM investigation of dislocation interactions in WC, Int J Refract Met Hard Mater 41 (2013) 416-421. [19] X. Liu, J. Zhang, C. Hou, H. Wang, X. Song, Z. Nie, Mechanisms of WC plastic deformation in cemented carbide, Mat Design 150 (2018) 154-164. [20] X. Liu, H. Wang, L. Wang, C. Hou, X. Song, X. Liu, X. Han, In situ study of fracture behavior of ultrafine WC–Co cemented carbide, Mat Res Lett 5 (2017) 55-60. [21] M. Lu, H. Russel, H. Huang, Fracture strength characterization of protective intermetallic coatings on AZ91E Mg alloys using FIB-machined microcantilever bending technique, J Mater

of

Res 30 (2015) 1678-1685.

[22] S. Massl, W. Thomma, J. Keckes, R. Pippan, Investigation of fracture properties of

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magnetron-stuttered TiN films by means of a FIB-based cantilever bending technique, Acta

-p

Mater 57 (2009) 1768- 1776.

[23] J.M. Gere, B.J. Goodno, Mechanics of Materials, 8th edition. Stamford: Cengage Learning;

re

2013.

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[24] D.A. Sandoval, A. Rinaldi, J.M. Tarrago, J.J. Roa, J. Fair, L. Llanes, Scale effect in mechanical characterization of WC-Co composites. Int J Refract Met Hard Mater 72 (2018) 157– 162.

na

[25] M.G. Gee, K. Mingard, B. Roebuck, Application of EBSD to the evaluation of plastic deformation in the mechanical testing of WC/Co hardmetal. Int J Refract Met Hard Mater 27

ur

(2009) 300–312.

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[26] E. Tarleton, D.S. Balint, J. Gong, A.J. Wilkinson, A discrete dislocation plasticity study of the micro-cantilever size effect. Acta Mater 88 (2015) 271-282. [27] J. Gong, A.J. Wilkinson, Anisotropy in the plastic flow properties of single-crystal α titanium determined from micro-cantilever beams. Acta Mater 57 (2009) 5693-5705. [28] H. Yu, G.B. Thompson, C.R. Weinberger, The role of chemistry and bonding in regulating fracture in multiphase transition metal carbides and nitrides. Ext Mech Lett 17 (2017) 1-6. [29] M. Lee, R.S. Gilmore, Single crystal elastic constants of tungsten monocarbide. J Mater Sci 17 (1982) 2657-2660. [30] T. Csanádi, S. Grasso, A. Kovalčíková, J. Dusza, M. Reece, Nanohardness and elastic anisotropy of ZrB2 crystals. J Eur Ceram Soc 36 (2016) 239-242.

24

Journal Pre-proof [31] D. Tromans, Elastic anisotropy of hcp metal crystals and polycrystals. Int J Rec Res Appl Stud 6 (2011) 462-483. [32] S.A.E. Johansson, M.V.G. Petisme, G. Wahnström, A computational study of special grain

Jo

ur

na

lP

re

-p

ro

of

boundaries in WC-Co cemented carbides. Comp Mat Sci 98 (2015) 345-353.

25

Journal Pre-proof Table 1

Beams

Composition of beams

Orientation of single WC

L-x2 (μm)

a (μm)

b (μm)

ma (μm)

x1 (μm)

A

single WC

Φ=11.1°

9.32

3.15

1.61

1.22

0

B

single WC

Φ=7.5°

15.09

3.52

1.31

1.50

0

C

single WC

Φ=66.9°

15.20

3.74

2.27

1.71

0

D

WC grains

-

10.11

3.15

1.70

1.48

1.4

E

WC grains

-

20.31

3.80

1.83

F

WC grains

-

17.63

3.82

1.71

G

WC grains

-

13.65

3.00

H

WC grains + Co

-

12.47

3.19

I

single WC

Φ=40.5°

12.92

J

single WC

Φ=81.2°

K

WC grains

-

L

WC grains

-

M

single WC

N O

Location of boundaries from the clamping (μm)

E (GPa)

σ (GPa)

-

WC ‘defect free’

795

20.5

-

WC ‘defect free’

833

14.6

-

WC ‘defect free’

532

11.1

5.3 (WC/WC)

WC ‘defected’

341

7.7

f o

ro

-p

e r P

Location of fracture

1.64

13.8

13.8 (WC/WC)

WC/WC

545

2.2

1.68

5.5

5.5 (WC/WC)

WC/WC

774

3.2

1.23

3.9

3.9 (WC/WC)

WC/WC

459

3.2

1.27

2.1

2.1 (WC/Co)

WC/Co

290

3.7

1.59

1.14

0.2

-

WC ‘defect free’

655

11.8

11.07

rn

1.65

3.19

1.70

1.31

0.6

-

WC ‘defected’

504

9.8

l a

1.46

u o

2.96

17.99

4.00

2.14

1.62

2.0

2.0 (WC/WC)

WC/WC

474

8.4

17.16

4.02

1.45

1.95

0

7.4 (WC/WC)

WC ‘defect free’

422

11.7

Φ=57.2°

18.90

3.95

2.14

1.73

0

-

WC ‘defect free’

584

11.2

WC grains + Co

-

15.33

3.36

1.87

1.33

7.5

2.3 (WC/Co), 7.5 (WC/WC)

WC/WC

374

3.5

WC grains + Co

-

16.75

3.85

2.38

1.72

1.2

1.2 (WC/Co)

WC/Co

470

5.8

J

26

Journal Pre-proof Figure and table captions:

Fig. 1: Schematic of an as-fabricated microcantilever with a pentagonal cross-section, which fractures at x=x1 due to the applied load of F at a distance of x2 from its free end. Fig. 2: The microstructure of the WC-Co composite tested: a) EBSD image with the outline of beams, b) SEM image with the as-prepared microcantilevers. c) Inverse pole figure legend of the WC grains corresponding to the EBSD map and schematic representation of the crystal

of

orientation relative to the sample coordinate system [11]. d) Inclined view of a typical

ro

microcantilever with a pentagonal shape cross-section.

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Fig. 3: Fracture of microcantilevers in WC grains: a) stress-strain curves corresponding to the upper surface of the beams at the facture site calculated from the measured load-displacement

re

data, b) schematic of the fracture origins in the WC grains, c)-e) top and f)-i) inclined view SEM

lP

images of the fracture surfaces.

Fig. 4: Fracture of microcantilevers at the boundary of WC grains: a) stress-strain curves

na

corresponding to the upper surface of the beams at the fracture site calculated from the measured load-displacement data, b) schematic of fracture origins at the WC boundaries, c) outline of a

ur

beam FIB milled from two WC grains with d) the corresponding top view SEM image of the

Jo

broken surface. e)-g) Inclined view SEM images of the different fracture surfaces. Fig. 5: a) Orientation dependence of Young’s modulus of WC grains measured by microcantilever bending tests and estimated from single crystal elastic constants [29]. b) The influence of beam composition on the Young’s modulus of microcantilevers in the tested WC-Co composite.

Fig. 6: Fracture strength of WC grains, WC/WC and WC/Co boundaries in WC-Co composites measured by microcantilever and microtensile testing [9,10,15]. Note that strength data for low energy WC/WC grain boundaries are estimated values since those were found to be at least as strong as the WC grains [15]. 27

Journal Pre-proof Tab. 1: The geometry and composition of each FIB milled microcantilever, the location of fracture during bending test, and the corresponding Young’s modulus (E) and fracture strength

Jo

ur

na

lP

re

-p

ro

of

(σ) values.

28

Journal Pre-proof Author statement: T. Csanádi designed the experimental plan, performed microcantilever bending and carried out the calculations and data evaluation. M. Vojtko prepared the microcantilevers and performed the sample characterization by SEM. J. Dusza provided ideas and direction for the research and contributed to the interpretation of results. The manuscript was written by T. Csanádi. All authors

Jo

ur

na

lP

re

-p

ro

of

reviewed the manuscript.

29

Journal Pre-proof Declaration of interests

Manuscript title: Deformation and fracture of WC grains and grains boundaries in a WC-Co hardmetal during microcantilever bending tests

Authors:

ro

of

Tamás Csanádi, Marek Vojtko, Ján Dusza

ur

Dr. Tamás Csanádi

Jo

Yours sincerely,

na

lP

re

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☒The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

30

Journal Pre-proof

Table 1 Orientation of L-x2 single WC (μm)

a (μm)

b (μm)

ma (μm)

x1 (μm)

Location of boundaries from the clamping (μm)

Location of fracture

E (GPa)

single WC

Φ=11.1°

9.32

3.15

1.61

1.22

0

-

WC ‘defect free’

795

single WC

Φ=7.5°

15.09

3.52

1.31

1.50

0

-

WC ‘defect free’

833

single WC

Φ=66.9°

15.20

3.74

2.27

1.71

0

-

WC ‘defect free’

532

WC grains

-

10.11

3.15

1.70

1.48

1.4

5.3 (WC/WC)

WC ‘defected’

341

WC grains

-

20.31

3.80

1.83

1.64

13.8

13.8 (WC/WC)

WC/WC

545

WC grains

-

17.63

3.82

1.71

1.68

WC grains

-

13.65

3.00

1.46

1.23

WC grains + Co -

12.47

3.19

1.65

1.27

ro

of

Composition of beams

5.5 (WC/WC)

WC/WC

774

3.9

3.9 (WC/WC)

WC/WC

459

2.1

2.1 (WC/Co)

WC/Co

290

re

-p

5.5

Φ=40.5°

12.92

2.96

1.59

1.14

0.2

-

WC ‘defect free’

655

single WC

Φ=81.2°

11.07

3.19

1.70

1.31

0.6

-

WC ‘defected’

504

WC grains

-

17.99

4.00

2.14

1.62

2.0

2.0 (WC/WC)

WC/WC

474

WC grains

-

17.16

4.02

1.45

1.95

0

7.4 (WC/WC)

WC ‘defect free’

422

single WC

Φ=57.2°

18.90

2.14

1.73

0

-

WC ‘defect free’

584

na

lP

single WC

3.95

15.33

3.36

1.87

1.33

7.5

2.3 (WC/Co), 7.5 (WC/WC)

WC/WC

374

WC grains + Co -

16.75

3.85

2.38

1.72

1.2

1.2 (WC/Co)

WC/Co

470

Jo

ur

WC grains + Co -

31

Journal Pre-proof Highlights:  Deformation and fracture behaviour of constituents of a WC-Co hardmetal were investigated by microcantilever bending technique combined with SEM and EBSD analyses.  The Young’s modulus of WC grains exhibited orientation dependence in the range of about 800-500 GPa in agreement with the theoretical prediction.  The WC grains showed plasticity before their final failure and their fracture strength (σ=12.3±3.8 GPa)

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is controlled by the interaction of dislocations and nanometre size defects.

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 The majority of boundaries in a WC-Co composite were found to be brittle high energy WC/WC

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boundaries and their fracture strength (σ=4.1±2.4) is generally much lower than that of WC grains.

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