Edge toughness of tungsten carbide based hardmetals

Accepted Manuscript Edge toughness of tungsten carbide based hardmetals

A.J. Gant, R. Morrell, A.S. Wronski PII: DOI: Reference:

S0263-4368(17)30842-9 https://doi.org/10.1016/j.ijrmhm.2017.12.020 RMHM 4618

To appear in:

International Journal of Refractory Metals and Hard Materials

Received date: Revised date: Accepted date:

9 November 2017 15 December 2017 16 December 2017

Please cite this article as: A.J. Gant, R. Morrell, A.S. Wronski , Edge toughness of tungsten carbide based hardmetals. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Rmhm(2017), https://doi.org/ 10.1016/j.ijrmhm.2017.12.020

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ACCEPTED MANUSCRIPT Edge Toughness of Tungsten Carbide Based Hardmetals AJ Gant*1, R Morrell2, AS Wronski3 *corresponding author 1 Element Six, Fermi Avenue, Harwell, Oxfordshire OX11 0QR, UK 2 National Physical Laboratory, Teddington, Middlesex TW11 0LW, UK 3 University of Bradford, Bradford, West Yorkshire, BD7 1DP, UK

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Keywords Hardmetal, toughness, test method

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Abstract

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Edge flaking of WC-based hardmetals has been examined in detail. So-called "edge toughness"; the load at which a flake will form under load vs. displacement from the specimen edge has been correlated with more commonly used toughness parameters; Palmqvist toughness, plane strain fracture toughness (KIC) and critical strain energy release rate (GIC). KIC and GIC showed better correlations than Palmqvist, though coarser grained hardmetals, exhibiting rising R-curves, were consistently found to be outliers. It is thought that this behaviour is consistent with far more pronounced crack bridging in these materials in the edge fracture mode. Mechanical property data were complimented by SEM microscopy to examine fracture behaviour in more detail.

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Introduction

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The work reported herein has been conducted for two principal reasons. Firstly, to further the understanding of an alternative toughness parameter which can be applied to brittle materials which has the potential to be easy to measure and does not require the complex geometries and technical difficulties associated with more traditional notched beam samples. Palmqvist toughness is commonly used measure of resistance to crack propagation in brittle materials such as technical ceramics, cermets and hardmetals. However, Palmqvist toughness is not universally applicable to tungsten carbide hardmetals; in some materials discrete measurable cracks are not produced from the corners of Vickers indentations. In some cases it is possible to ameliorate this by increasing the force on the indenter, but at high loads chipping of the indenter can and does occur. Also, due to scaling effects in hardness measurement, increasing loads means the results are not universally applicable. The second driver for exploring edge chipping further is quality assurance in the hardmetal industry. The transverse rupture test (TRS) is well established as a benchmark mechanical property test, but suffers from several drawbacks. Amongst the latter are a lack of discriminability and also the need for large sample batches to be tested to give a set of results that can be regarded as being representative of the whole population. Such large sample batches are expensive to produce and despite such advances as automated bend testing without the need for an operator, the overall cost is high. Edge chipping offers the potential of providing populations of mechanical data which do not require the sample volumes and degree of preparation which TRS entails.

ACCEPTED MANUSCRIPT Background to Edge Toughness

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Although edge toughness, as it is recognised as such today, has only been reported on in approximately the last fifteen years [1-4], similar, but not identical, processes have been conducted since Neolithic times. Flint knapping was practised as a means of producing sharp stone tools such as axeheads. Flint knapping is essentially a form of conchoidal flake formation [5,6]. Flints are knapped by being struck near an edge with a hard stone, often with a glancing blow, the process either producing large flakes for use as scrapers or knives, or small flakes which go to waste as a larger tool, such as an axehead, is shaped. Pressure flaking was also practised in Neolithic times; the splitting of large flints into shards of greater utility.

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Modern day hard materials such as ceramics, hardmetals and some metal alloys are also brittle. In engineering applications, edges on such materials are therefore at risk from chipping, which may have a deleterious effect on component utility. To mitigate this, edges are often chamfered; effectively blunting them, e.g. for applications such as engine valves [7], but minimal chamfering is often desirable, particularly for cutting operations. There is a continual drive to improve toughness to boost materials’ damage tolerance.

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The measurement of “toughness” of modern, technically important, brittle materials is often fraught with difficulty, whether in the laboratory or the field. Conventional methods of assessing toughness of ceramics, usually by means of one of the standardised plane strain fracture toughness tests (SENB, SEVNB etc), produce KIC values which sometimes cannot be entirely divorced from the test method. In some respects the assessment of toughness in hardmetals is possibly even more problematical; perhaps the simplest test method for the assessment of toughness in this material type is the indentation technique via the generation of Palmqvist cracks. The recent appearance of very fine sub-micrometre grained hardmetals has given rise to enhanced problems; the toughness of the very materials in which manufacturers have possibly most at stake in the hardmetals sector are proving difficult to assess by this convenient method. This is the context in which a test programme was initiated to assess further the edge toughness of hardmetals. The Process of Edge Chipping

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When a hard indenter is loaded onto the surface of a brittle material, the material’s response is a combination of plastic deformation and fracture. The more plastic the material, the larger the indentation, and the less the degree of fracture produced. In ceramic materials with low values of toughness, indentation is accompanied by local fragmentation as well as by well-defined cracks. With a standard Vickers diamond indenter, cracks appear from the corners of the indentation at forces above about 2 N, and with a standard Knoop diamond, at forces above about 5 N. In a low toughness material, the cracks develop into a half-penny shape beneath the indenter, but as the toughness increases to about 6 - 8 MPa m1/2, the cracks become restricted to the immediate surface (Palmqvist cracks). If a blunt indenter, such as a Rockwell type (0.2 mm tip radius), is used, randomly positioned radial cracks develop at forces above about 20 N. If the contact radius of curvature exceeds about 1 mm, the dominant mode of cracking become Hertzian, i.e. ring cracks, at much higher force levels. Hertzian crack systems have been found to initiate in single crystal synthetic

ACCEPTED MANUSCRIPT diamond (regardless of crystallographic orientation) edge flaking experiments [8], where the tensile stress at the boundary of the contact region is reached before the shear strength is reached below the indenter.

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If the indentation is made near an edge, the stress field is modified by elastic relaxations of the edge face. Instead of the stress field decaying sharply with distance from the indentation centre, it becomes easier to propagate the cracks, particularly those running parallel to the edge or towards it. When a critical force is exceeded, the cracks run out at the edge, and a flake is formed (Figure 1).

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Figure 1: Indenting near an edge causes the radial cracks running approximately parallel to the edge to veer towards the edge to form a flake.

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Experimental work [2,9] has shown that for many fine-grained brittle ceramics, there is a linear relationship between the chipping load and the distance of the indenter from the edge. The slope of this relationship, which has units of N/m, dimensionally the same as fracture energy, has been termed the ‘edge toughness’, the value of which generally increases with increasing conventional toughness. That edge toughness is related to conventional KIC has been demonstrated by correlation with separately determined toughness data [2,3]; for a wide range of material types from brittle plastics to hardmetals the best fit having been between edge toughness and GIC. The explanations for this behaviour are by no means clear. The complexity of the stress field has not to date permitted a unique ‘calibration’ of this test as a direct measure of toughness. McCormick and Almond’s analysis work [2] showed a number of important features: 1. The edge displacements measured experimentally matched well a two-dimensional analytical model constructed by assuming the Rockwell indentation to be equivalent to an eccentric pressurised pipe with the outer radius infinite. It was also shown that the maximum hoop stress around the indentation occurred at two symmetrical positions (shown schematically in Figure 2), explaining the initiation angles of the flaking cracks. In addition, when the indentation became close to the edge, a tensile stress maximum developed along the edge. This explains occasionally seen split flakes.

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2. The stress field in a two-dimensional section through the edge and the indentation is difficult to solve analytically, especially in the presence of a crack, but finite element analysis has shown that the stress field becomes skewed towards the edge, imparting a curvature to the running crack, hence the curved nature of flakes. 3. The flake shape is broadly constant [1], independent of size and hence of distance of indentation from the edge. It is this feature that has been used to explain why the flaking load scales linearly with distance from the edge, unlike other related fracture mechanical situations, such as in indentation fracture and in the double cantilever beam geometry of fracture toughness specimen. In both of these latter cases, there is non-linearity with increasing dimensions. However, there is no analytical proof that indentation flaking should scale linearly. Thouless, Evans, Ashby and Hutchinson [9] found a linear relationship for the distributed pressure flaking of pre-notched plates in a two-dimensional situation, and showed that this could be expected through an asymptotic solution for short initial cracks. However, this solution did not involve the complexities of indentation nor the threedimensional shape of indentation edge flakes. 4. Under an increasing indentation force, cracks normally develop and grow stably and steadily into a declining stress field. The instability of flake formation must result from an inflection in the stress field as the edge is approached. Once a critical position is reached the crack runs out to the surface. However the location of this position remains unclear, but is presumably between 50 and 70% of the final crack length. 5. The edge angle is important in defining the chipping force. As the angle becomes more obtuse, the chipping force rises rapidly. It is this fact which explains the effectiveness of chamfering. The presence of a chamfer shifts the possible contact position of a damaging point force further into the material. It can be also be deduced that tougher materials need smaller chamfers than less tough ones. The fracture process that occurs on indentation is controlled by the local microstructure, and thus gives rise to some variability in behaviour. If a crack initiates and moves steeply towards an edge, the flake will be narrow; while if it moves essentially parallel with the edge, it will become wide in that direction. Often the result is flake asymmetry, but despite this, at a given indentation distance from the edge the scatter in flaking force is low, typically less than  10% about the mean. The evidence for a linear fit between flaking force and distance from edge is statistically strong when using a Rockwell indenter [9].

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ACCEPTED MANUSCRIPT Figure 2: Analytical evaluation of the two-dimensional stress field around a pressurised hole near the edge of a plate gives the maximum hoop stresses at A and B, with a further stress peak at C growing with decreasing distance from the edge. Experimental Procedure Materials

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WK(100), MNm-3/2 dCo, µm dWC, µm wt% binder HV30 6 1358 10.46 0.64 1.37 7 1836 9.56 0.13 0.26 (Co/Ni) 5 1836 9.55 0.17 0.38 (Co/Ni) 12 1557 10.44 0.19 0.25 6 1466 8.83 0.29 0.63 11 1294 13.03 0.55 0.86 11 1153 18.16 1.01 1.89 6 1450 10.37 0.56 1.13 6 1129 18.39 1.19 4.06 6 2010 9 0.08 0.17 11 981 28.94 2.27 4.04 6 1583 10.73 0.34 0.67 9 1712 10.06 0.18 0.32

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Grade mars6C NK07 shmcn5 shmcn12 mars6ANI mars11A mars11D mars6B mars6E shm220 mars11E mars6A macn9

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Constituent members of the British Hardmetal Research Group (BHRG) supplied a range of WC hardmetal samples (as detailed in Table 1), of dimensions 50 x 50 x 5 mm. The grades feature a cobalt binder, apart from shmcn5 and shmcn12 which are cobalt/nickel (the exact ratio of the two transition metals has not been disclosed to the authors). Note that dCo pertains to the binder linear intercept and that dWC pertains to the WC grain size intercept; WK(100) is the Palmqvist toughness with the results generated using a 100 kg force. A liquid jet erosion programme running simultaneously with the work reported herein dictated this sample size. The samples were surface ground using a resin-bonded grinding wheel of 165 m diamond grit to produce flat, parallel faces. This surface preparation was chosen as it is widely used in the hardmetal industry. They were then spark eroded into blocks 13 x 13 x 5 mm, with the spark eroded surface ground to these final dimensions. The samples were then annealed for one hour at a temperature of 800 ºC to remove residual stresses induced by surface grinding.

Table 1: Hardmetal inventory The tests were performed in a purpose-built testing machine, which permitted the peak force to be recorded, and which unloaded the indenter immediately upon flaking1. Test-pieces were clamped in a holder on an X-Y table, and the edge sighted using a small microscope centered on the axis of the indenter. Standard geometry Rockwell monocrystalline diamond indenters2 were used, since polycrystalline indenters were not available. All tests were performed at a cross-head rate of 0.5 mm/min, giving times to flake production of between 10 and 40 s depending on 1 2

The ET500, manufactured by Engineering Systems (Nottingham) Ltd, UK. Candover Diamond Tools Ltd, Andover, Hants, UK.

ACCEPTED MANUSCRIPT distance from the edge, which was varied between 0.15 and 0.30 mm. The separation between indentation positions was sufficient to ensure no overlap of flakes. The work reported herein is in two distinct parts: (a) Fixed Displacement Tests

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(b) Variable Displacement Tests

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The objective was to compare scatter in chip formation loads with that from individual Palmqvist crack lengths (the latter from a fixed load of 100 kgf; this load was necessary to produce cracks that were single discrete cracks emanating from the corners of a Vickers indentation). Only Palmqvist results in which cracks meeting the standard criteria emanating from all four corners of a Vickers indentation were used. Ten 100 kgf Vickers indentations were produced for each hardmetal grade in a concurrent project, giving 40 individual crack lengths. For statistical comparison, 40 edge flakes were produced in each hardmetal grade at a fixed displacement of 0.4 mm. For direct comparison the two sets of data for a given hardmetal grade were ranked and normalised according to their respective mean values, in order that the two respective ranked data sets might be plotted on the same axes for direct comparison.

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Tests were performed across a range of edge displacements; from 0.15 to 0.30 mm in 0.01 mm increments, with one chip test being conducted per increment in edge displacement. Chip formation loads were plotted with respect to edge displacement and curve fits made; the gradient of these plots being previously cited as “edge toughness”. Edge toughness values were calculated using Origin 2nd order polynomial curve fitting. These edge toughness values were then compared with other (more commonly used) mechanical parameters such as Palmqvist toughness WK100, critical strain energy release rate GIC and Vickers hardness HV30. These are dealt with in the results section.

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Results

Toughness limits for the test

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All hardmetals in the programme inventory (WK ranging from 9 to 28 MNm-3/2) could be tested using the edge toughness tester with a Rockwell diamond indenter, giving well-defined flakes of classical geometry [10]. Linearity of flaking load/distance from edge relationship This was examined earlier by Berthold, Nickel and Weisskopf [7] for a range of tungsten carbide hardmetals with flaking distances of up to 0.3 mm from the edge, and found to be the case (e.g. Figure 5). In the present work we have evaluated the materials in Table 1 over the edge distance range 0.15 to 0.3 mm, in 0.01 mm increments, using one flake for each edge displacement. Within the scatter for each type of material, this straight-line relationship is maintained, but with increasing toughness there is an increasing tendency for the data to display some apparent nonlinearity; in this case concave plots have been found. There appears to be no

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Figure 3: Edge chip loads vs displacement: hardmetal grade mars6ANi.

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Figure 4: Edge chip loads vs displacement: hardmetal grade mars6A.

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Figure 5: Edge chip loads vs displacement: hardmetal grade mars6B.

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Figure 6: Edge chip loads vs displacement: hardmetal grade mars6C.

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Figure 7: Edge chip loads vs displacement: hardmetal grade mars6E.

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Figure 8: Edge chip loads vs displacement: hardmetal grade mars11A.

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Figure 9: Edge chip loads vs displacement: hardmetal grade mars11D.

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Figure 10: Edge chip loads vs displacement: hardmetal grade mars11E.

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Figure 11: Edge chip loads vs displacement: hardmetal grade shmcn5.

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Figure 12: Edge chip loads vs displacement: hardmetal grade shmcn12.

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Figure 13: Edge chip loads vs displacement: hardmetal grade shm220.

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Figure 14: Edge chip loads vs displacement: hardmetal grade NK07. Re-evaluation of the ‘universal relationship’ Values of GIC have been computed with elastic modulus according to Doi, Fujiwara, Miyake and Osawa [11], an assumed Poisson ratio of 0.3, Palmqvist toughness data from NPL measurements and plane strain fracture toughness KIC from Sandvik Hard Materials (Coventry); the latter generated using an EXAKT 6000 EA automated machine. Figure 14a gives the mean edge toughness for each material (from linear fits to Figures 3 to 14), based on linear fits to the flaking load vs. distance from edge data.

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Figure 14a: Mean edge toughness as a bar chart; based on linear fits to the raw chipping data.

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The correlation between edge toughness and, respectively KIC and calculated plane strain GIC is given in Figures 18 and 19. With the exception of the Mars11E hardmetal, the data correlate reasonably in the KIC plot, but rather better in the GIC plot. The toughness data for high-toughness hardmetals are uncertain because of uncertainties in the use of the Palmqvist method and its sensitivity to residual surface stresses [12]. The veracity of this particular result requires re-checking with direct measurement of KIC; this has been undertaken by Sandvik Hard Materials as outlined above; details are given in the Appendix. Overall G1C appears to give the best correlation with edge toughness.

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Figure 16: Edge toughness vs Palmqvist toughness plot (100 kgf results used as only at this high applied load could cracks be initiated across the complete suite of hardmetals in the present study). 2200

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Figure 18: Edge toughness vs plane strain-derived critical strain energy release rate (GIC).

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Figure 21: Cumulative running average data at a fixed displacement of 0.40 mm. The 40 data points for a given material at a fixed displacement of 0.40 mm from the edge have also been taken in the order that they were generated so as to give a cumulative running average (see Figure 21) in order to assess the size of chip result population needed into order to give a reproducible mean results. The parameter is a type of finite impulse response filter used to analyze a set of data points by creating a series of averages of different subsets of the full data set. A moving average is not a

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Figure 22: shm220; 100 cumulative running average data at a fixed displacement of 0.40 mm.

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Fixed Displacement Test Statistics and Comparison with Palmqvist Crack Lengths

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Figure 23: Comparison of coefficient of variation based on 40 data points at 0.4 mm from the edge.

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Figure 24: mars6C mean-normalised edge flake load and Palmqvist crack length plot.

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Figure 26: shmcn5 mean-normalised edge flake load and Palmqvist crack length plot.

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Figure 32: mars6A mean-normalised edge flake load and Palmqvist crack length plot. One aspect which is of interest from the preceding figures is that the alternative binder materials, whether nickel or Co/Ni produce a distinctly bimodal distribution in fixed displacement edge flake loads. At present no explanation can be given for this. Note also that mars6A (fine grain, 6% cobalt) produces the closest fit in terms of rankings between the Palmqvist and the edge chip data. Effect of Grinding Direction Earlier work reported by Morrell and Gant [13] had shown that in sintered silicon carbide ceramics that at short edge displacements (< 0.25 mm), flake shapes were

ACCEPTED MANUSCRIPT very unusual. Examination of the crack trajectories showed that one side of the flake was strongly influenced by the original machining direction. Normally, no bias on shape had been found with machining direction for finely ground surfaces, but it was clear that in that instance, the grinding process was severe enough for the grinding cracks to initiate the flaking process. However, the actual flaking load for such cracks was not abnormal within the scatter of results.

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In the earlier work relatively little had been reported on WC hardmetals, and so the effect of grinding direction in these materials was not known. In the current work the mars6E hardmetal grade was selected at random to assess any possible effect of grinding. The results taken were at a fixed displacement of 0.4 mm. The grinding direction relative to the edge was noted and the mean and standard deviations for a given direction and also for the flake loads regardless of direction. The net result was that no systematic bias in the mean flake load. The statistics are summarised in Table 2. As can be seen, there are only negligible differences in both mean loads and standard deviations. Raw data are shown in Figure 33 and Figure 34. Perpenidicular Direction 732 53

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The majority of the more brittle materials showed either clean scars with little evidence of secondary processes or interruptions to the flaking crack development, or flakes, which had not detached (Figures 35 to 39). In most cases, the tougher materials also showed no flake detachment. It is presumed that failure to detach means that there is insufficient evolution of stored elastic energy in the machine and test-piece to result in rapid final propagation. Small flakes created at low forces were most likely not to detach completely. In all but the hardest/ most brittle hardmetals, the scar fractography showed that a shear mode had been operating in the early stages of chip formation (Figure 36), however the vast majority of the scars did show brittle fracture of a mixed transgranular/intergranular mode. There were no detectable differences in the proportions of transgranular and intergranular fracture according to location within the scar or with respect to material properties across the hardness/toughness spectrum.

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Figure 35: shm220- brittle initiation region.

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Figure 36: Mars6C- shear (ductile) initiation region.

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Figure 37: Overall view of flake initiation region in mars6C.

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Figure 38: Close up of fracture surface in flake initiation region in mars6C.

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In the course of generating the data reproduced earlier, a chart recorder was connected to the ET500 to check for any perturbations in the load/time plot as the sample was being stressed by the increasing indenter loads. Often small jumps in the plots were seen. Interruption of the test (raising the indenter free from the sample surface) revealed that microcracks were often evident, and sometimes microscopic spalling and plastic deformation. The microcracks had preferred orientations; heading towards points A and/or B as shown in Figure 2. The most brittle hardmetal grade, shm220 was selected for further study; pop-in of the aforementioned microcracks had been picked up using an acoustic emission detector, and having a loudspeaker plugged it, enabled the test to be curtailed once one or more audible “clicks” had been heard. The samples were thereafter examined by SEM, showing the presence of microcracks as described; SEM micrographs are reproduced here as Figures 39a to 39d. Notice in Figure 39b that there is a microcrack running into the bulk of the material in an approximate NNE direction, but is arrested due to the decaying stress field. That which has grown in a SSW direction in Figure 39c is also similarly arrested.

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Figure 39a: Subcritical damage events; shm220.

Figure 39b: Subcritical damage events; shm220.

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Figure 39c: Subcritical damage events; shm220.

Figure 39d: Subcritical damage events; shm220.

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Although the universal relationship between K1C/G1C and “edge toughness” previously shown to exist [13] for brittle materials ranging from glasses to tool steels has been shown to be applicable to hardmetals, the method does not give an accurate prediction of conventionally measured toughness, as noted by Chai and Lawn [14]. Their prediction of a power law relationship with an exponent of 1.5 between edge displacement and chipping load is not borne out by the current work. Reasons for this are not entirely clear, however, it has also been noted in an extensive study of dental ceramics [15]; it is postulated that at short (i.e. near-) edge displacements that mechanically the indenter behaves as a point load, rather the model discussed by McCormick and Almond [2] and later by Chai and Lawn [14]. However, sets of authors’ stress analyses do have self-similarity as a leitmotif. In this case, other factors may be at work; for example subcritical crack growth (and hence stress relief) from radial crack growth perpendicular to the free edge which can occur at short edge displacements.

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As to which of the more conventional toughness parameters is the best predictor of edge toughness, it would appear that G1C is marginally better, in line with Morrell and Gant’s findings [13], but at odds with those of Quinn, Su, Flanders and Lloyd [15]. It will be observed that regardless of whether K1C or G1C is used to compare edge toughness, there is a tendency for the coarser grained materials to lie to the right of the trend lines. Another observation regarding the coarser grained materials is that the flake load vs edge displacement plots are more strongly power law dependent than their finer grained counterparts. The stronger power law dependency in coarser grained brittle materials was also found by Quinn and co-workers when working with dental ceramics [15]. Petit, Vandeneede and Cambier [16] also noted a general trend in increased power law dependency with tougher aluminas and zirconias, but did not include grain size data, so R-curve effects are difficult to relate to directly in this case. It has previously been thought that both the more pronounced power law behaviour and also the K1C/G1C- edge toughness trend line behaviour are attributable to rising Rcurve behaviour [14]. Specifically here the concept of a rising R curve is pertinent; a plot of plane strain fracture resistance (KIR) vs. crack extension where the fracture resistance increases as a crack grows over a length range which is appropriate to LEFM. In short, effective fracture toughness is not linearly invariant with crack lengths when describing the attributes of long cracks. R-curves for the present materials are shown in Figure 40. The fracture toughness tests were conducted on 3 x 4 x 25 mm +/- 0.1 mm samples, into which a notch approximately 2.2 mm long was produced with a notch 2.65 mm long, radius of 2.657 µm. Cracks initiated from the notch were extended up to 275µm during loading. It will be observed that the most pronounced spatially non-variant fracture resistances are produced by those hardmetals having a high initial KIR, and within the three toughest grades, the most steeply rising plot is that of the hardmetal grade with the coarsest microstructure (in terms of WC grain size and binder linear intercept, as this sub-group all contain 11% wt. cobalt).

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However, in the present study, there is seen to be no systematic correlation between R curve behaviour and the tendency of edge chipping load vs displacement to exhibit power law behaviour. Although little systematic work has been reported on R-curve behaviour in WC based hardmetals, Felten [17] found that both coarse WC grains and large (ductile) binder fractions promote more pronounced R-curve behaviour; the net effect in both cases being to increase binder linear intercept (i.e. the ductile ligaments in terms of crack-tip shielding); though exact relationships with binder linear intercept were not explored. However, it was noted that R-curves in hardmetals plateau out at around 300 µm (which fortuitously just greater than the maximum measurable crack lengths produced in the present study and illustrated in Figure 40). Crack tip bridging models in WC/Co assume that a cobalt bulk flow stress is based on its uniaxial yield strength, however in combined mode I+II loading, there is also a shear component to the plastic work of the cobalt ligaments preceding fracture; the latter implies also a differing crack tip opening displacement (CTOD). Indeed, this has been found by FEM simulation by Patle [18]. Binder void formation in mode I loading is predicted by a criterion combining intense strain and a high hydrostatic-deviatoric stress [19]. However, in the present study, the void formation mechanism may be modified by the somewhat different triaxality in combined mode I+II. Also of note here is Gomes,Wronski and Wright’s finding [20] that more steeply rising R-curves in practice means reduced sensitivity of the progression of the Rcurve to initial defects; in effect an indicator of damage tolerance.

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Chai and Lawn [14] noted that a key simplifying feature in the power law derivation is that the scaling of the critical depth cF for chipping with the contact location; it may be the case that the scaling is not universally applicable; this is one implication of Rcurve behaviour. Both the Chai and the McCormick approaches feature selfsimilarity; this is inherent in the critical depth scaling in Chai’s work. However, if flake geometry (i.e. surface area) differs from one material (or indeed from one test to another in a given material) to another, the critical depth approach has to be modified to take this into account. McCormick and Almond [2] and Petit, Vandeneede and Cambier [16] alluded to this, with the former normalizing the crack length by a flake size parameter, which would be spatially variant in practice, but could be considered to be one-dimensional for most purposes. McCormick and Almond [2] published a figure showing a natural tendency of short subcritical cracks formed early in the loading cycle under the indenter (in the expected chip formation direction) to be arrested as the stress field decayed. This is reproduced here as Figure 41.

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Figure 41: Plot of normalised crack depth (c) against the KIC for different loads. The crack will grow unstably at load F2 from point x–y. Then the crack will grow stable as the load is increased from F2 to F3 until point Z at which point the crack growth is unstable again [2]. However in the original analysis (as per Figure 41) there is an underlying assumption that KIC is invariant with crack length. Rising R-curve behaviour is essentially stating that fracture resistance is not invariant with crack length, hence the separation between F2 and F3 will increase (indicated by the vertical arrow) and there will be a concomitant increase in the Y-Z crack length differential. Rising R-curve behaviour (as reported for mode I cracks propagating under plane strain conditions) may not be the only factor in the deviation of the coarser grained materials from the K1C/G1C- edge toughness trend line; a fact overlooked by many authors is that the fast fracture mode towards the final stages of chip detachment is mixed mode (i.e. mode I + mode II), thus a shearing component is present. Saveker reported [21] conducted a series of single edge notched beam (SENB) and edge toughness experiments on two variants of hot isostatically pressed ASP30 high speed

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steel quenched and tempered to 65 HRc; one variant was a standard composition, but the other featured a 0.05% (wt.) particulate titanium diboride (TiB2) addition. The latter changed to a complex boride during HIPing as fortuitously the HIPing temperature approximated to that of the iron-boron eutectic (1149°C) [22]. The net result was that the steel matrix immediately surrounding the complex boride was substantially denuded of alloying elements, giving rise to softer (easy to shear) discrete zones in the general steel microstructure. SENB experiments indicated no apparent change in K1C with the boride addition. Edge chipping experiments were successfully conducted on the standard specification material, but could not be done on the boride variant due to intense shear. It may be the case that although the effect of binder ligament dimensions on K1C in hardmetals is well-known, their effect on edge toughness due (a) to their relatively easy ability to shear and (b) the occurrence mixed mode (I+II) fast fracture which will be operative as the propagating crack advances (curves) to the free surface. In the case of the latter, due to lack of constraint, the plastic zone size is larger than that for plane strain given by the IrwinMcClintock relationship [23]; the implication being that local microstructural shear ligaments will have a greater toughening effect under non plane strain conditions than under plane strain conditions. The converse argument, that for relatively short (relative to plastic zone size rp) cobalt ligaments, the plastic zone size would, in an ideal scenario, exceed the binder intercept, but is always constrained by it, regardless of whether undergoing mode I fracture or mixed mode (I+II) cracking. In hardmetal grades with coarse binder intercepts, the plastic zone does not always reach the same dimensions as the binder intercept [24]. In short, it is postulated that for small dCo, the local critical stress intensity factor Kc in mode I (opening) is not dissimilar to that in mode II (shear), whereas with longer binder ligaments, the local critical stress intensity factor may differ significantly according to loading mode.

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A distinct lack of correlation was found between microstructural parameter distributions (binder and WC grain size linear intercept standard deviations) and those of flaking loads at a fixed edge displacement; this is thought to result from local microstructural variations not having a significant influence on fast fracture

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Wherever possible authors have used plane strain fracture toughness as a comparator with edge toughness, using a recognised method; single edge notched beam (SENB). However, hardmetals have been problematic when it comes to measurement of K1C; namely control of precrack length within the required parameters dictated by the relevant standard. For this reason, indentation (Palmqvist) toughness is commonly used in its stead. Despite the Palmqvist parameter WK being essentially a crack arrest parameter [25], it is reported to show good agreement with K1C up to K1C values of approximately 15-18 MPam1/2 and above [26]. In the present study, edge toughness has been compared with Palmqvist toughness. However, inspection of the hardmetal inventory toughness values reveals that several grades have a WK value of 18 MPam1/2 or above (mars6E, mars11D and mars11E). Exner [27] showed that at such high toughness, the indentation method effectively overestimates a value for K1C. If Exner’s relationship is used to give an estimated value for K1C on the basis of indentation toughness, the high toughness hardmetals are disproportionately moved to the left in the plots shown in the K1C -edge toughness and G1C -edge toughness plots. In terms of scar fractography, no change in WC grain fracture (transgranular vs intergranular etc) could be detected, which is in broad agreement with Exner’s [27]

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findings, in which a change in crack velocity between stable and unstable cracks could not be inferred from fractography or based on binder volume fraction or WC grain size. Palmqvist cracks in WC hardmetals cannot be considered as intrinsic material defects by any means. However, their short length and decreasing crack driving force, making it essentially a crack arrest parameter, at least give some indication of the variability of short crack behaviours in WC/Co. An inverse correlation might therefore be postulated between variance in Palmqvist crack length in a given hardmetal grade and slope of the respective R-curve, however, this hast not be proven herein. However, the question also arises as to at what point in the edge fracture process is the sharp drop in resultant force on the hardmetal block recorded.

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Caution must also be exercised when using a comparative approach to toughness evaluation for other reasons. Firstly there is no data available on edge crack propagation rates and their magnitude relative to those produced under SENB, SEVNB or indentation conditions; fracture stress in hardmetals is influenced by loading rate [26] as with more brittle materials such as glasses and technical ceramics. Secondly, due to its intrinsic geometry, mixed mode fracture will occur in later stages of the chipping process. The implications for shear resistance have already been alluded to. However, another fundamental difference between plane strain toughness testing and the edge fracture process is that crack bridging [27-29] may have a disproportionate effect due to the mixed mode rather than pure mode I crack propagation (effectively creating a shear-resistant “mechanical key”). Crack bridging can be readily seen in indentation toughness testing of hardmetals and is more pronounced in the coarser WC grain materials [30], though crack bridging, being a long-range (on the microstructural scale) toughening mechanism [30], may not attain its full potential in a test producing short range Palmqvist cracks.

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A marginally better correlation was found between edge toughness and G1C; than with K1C; however earlier work had investigated a broader toughness spectrum together with vastly different modulus values in a disparate set of materials [11]. In some aspects, the application of LEFM, or at least to plot “edge toughness” vs KIC may be of limited validity. This is in part due to the plasticity under the indenter as it is progressively loaded in compression; in this case the approach of Irwin [31] may be more appropriate, and hence from the strain energy consideration viewpoint, may at least, in part, explain the superior correlation of GIC rather than KIC with the edge toughness parameter. It should also be noted that critical strain energy release rate and edge toughness are dimensionally equivalent; both parameters can be described in force/distance units (energy/area units of GIC can be reduced by dimensional analysis to force/distance). However, a word of caution on the (apparent) G IC- edge toughness correlation; it only appears to correlate where the degree of microplasticity in a set of materials is comparable; Quinn and Quinn [32] found this when comparing technical ceramics and ceramic matrix composites (CMCs) with ceramic/glass resin composites; the latter were found to show a pronounced divergence from the edge toughness/GIC trend line. Although Chai and Lawn’s fracture mechanics analysis resulting in the edge displacement/flake load power law appears theoretically sound, in practice experimental results can deviate from it for several reasons; the most fundamental that it is made explicit that critical stress intensity Kc is single valued and crack-size

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independent, which is valid for fine-grain materials which do not exhibit rising Rcurve behaviour [33]; this is clearly not applicable to coarse grained and high binder volume fraction hardmetals [17]. In the current work, a Rockwell indenter was used. This type of indenter is not self-similar; self-similarity is an inherent assumption in Chai and Lawn’s power law derivation. Also, as Quinn [15] pointed out, at short edge displacements, up to 25% of the displacement is occupied by the indenter impression. However, in the present study, flake initiation position (edge displacement) was accurately predetermined, unlike Gogotsi [34,35] who measured edge displacement from the remote face of the indentation impression, thus introducing significant error, especially at short edge displacements. It would appear that the pseudo-linear flaking load/displacement relationships are a consequence of indenter geometry and/or relatively short edge displacements being employed; no irrefutable fracture mechanics arguments have to date been published in support of the experimental linear behaviour found by a number of authors.

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Rate effects can also lead to an underestimation of the true equilibrium value of Kc; static fatigue effects are known in ceramics, where in indentation tests, radial cracks can grow in a controlled manner on or after loading [36], and environmental stress fracture be feasible in hardmetal [28].

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Only in some fine-grain materials was there a good fit in ranked normalised results between Palmqvist crack lengths and flaking loads results; in terms of toughness, good fits were obtained well below the 15-18 MPam1/2 region where indentation fracture toughness and plane strain fracture toughness relationships begin to deviate from linearity [25,27].

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Effect of compliance; compliance is a factor noted by McCormick [2] and by Gogotsi [35] and is affected by local instantaneous flake shape and size and material Young’s modulus. Modulus for a given material is naturally a fixed parameter, but compliance changes with edge crack geometry as it grows. The role of modulus may account for the traditionally better correlation seen between G1C and edge toughness rather than that of K1C. To date no fracture mechanics analyses have been explored to further understanding of the G1C -edge toughness relationship. More recent authors [15,30,34] have refuted the existence of the relationship, however, close inspection of their results reveal that the toughness spectrum investigated was narrow compared with the earlier studies of McCormick [2] and Morrell [13]. Conclusions 1. A combination of linear and non-linear edge displacement vs chipping load plots were found. For a given hardmetal composition (6% Co or 11% Co) there appears to be a slight tendency to produce non-linearity in the coarser WC grain (i.e. tougher) materials; this may be related to rising R-curve behaviour.

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3. Local microstructural variations as characterized by standard deviation in the WC grain and the binder linear intercepts do not influence scatter in the chipping load data at a fixed displacement; again it is thought that as the load recorded is derived from a fast fracture/ long crack regime, occasionally found localised microstructural inhomogeneities will have little influence.

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4. At a fixed edge displacement it has been shown that running average chipping load data achieved reasonable convergence after 40 data points.

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5. Re-evaluation of the “universal relationship” between Palmqvist-derived critical strain energy release rate GIC /KIC and “edge toughness” has shown that WC grain size has a subtle effect, with finer-grained materials appearing (in general) to lie to the left of both master plots.

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6. Ranked mean normalised distributions of Palmqvist crack lengths and fixed displacement chipping loads showed good correlations in the mars6A, mars6C and mars11A grades, but not in the others. Reasons for this are not clear at the present time, but may be related to variability in flake shape/surface area.

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To Mike Carpenter and Y. Cui of Sandvik Hard Materials, Coventry for conducting plane strain fracture toughness testing to provide comparative data. To Eric Bennett and Petra Mildeova of NPL for producing the Palmqvist toughness data.

ACCEPTED MANUSCRIPT References [1] Almond E.A. and McCormick N.J., Constant geometry edge-flaking of brittle materials, Nature 1986; 321: 53-4. [2] McCormick N.J. and Almond E.A., Edge flaking of brittle materials, Journal of Hard Materials 1990; 1, 25-51. [3] McCormick N.J., Edge flaking as a measure of material performance, Metals and Materials 1992; March, 154-6.

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[4] Danzer R. and Paar R., Edge strength of brittle materials, Fortschrittberichte der Deutschen Keramische Gesellschaft, 1994,10, 3, 77-84.

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[5] Speth J.D., Mechanical basis of percussion flaking, American Antiquity 1972, 37: 34-60. [6] Cotterell B., Kamminga J., and F P Dickson, The essential mechanics of conchoidal flaking, International Journal of Fracture 1985; 29: 205-21.

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[7] Berthold C., Nickel K.G., Weisskopf K.L., A device for testing the edge flaking of ceramic valves, cfi/Berichte der Deutschen Keramische Gesellschaft 1996; 73: 9: 5313.

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[8] Zaayman E., Morrison G., Field J.E., Edge flaking in diamond, International Journal of Refractory Metals and Hard Materials, 2009, 27, 409-416.

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[9] Thouless M.D., Evans A.G., Ashby M.F. and Hutchinson J.W., The edge cracking and spalling of brittle plates, Acta Metallugica 1987; 35; 6: 1333-41.

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[10] Lardner, T.J., Ritter, J.E., Shiao, M.L., Lin, M.R., Behavior of indentation cracks near free surfaces and interfaces, International Journal of Fracture 1990, 22, 133-143.

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[11] Bolton, J.D., Keely, R.J., Fracture toughness (K1C) of cemented carbides, Fibre Science and Technology 1983, 19, 37-58.

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[12] Doi H., Fujiwara Y., Miyake K., and Osawa Y., A systematic investigation of elastic moduli of WC-Co Alloys, Metallurgical Transactions 1970; 5: 1417-25. [13] Morrell R., and Gant A.J.; Edge chipping of hard materials, International Journal of Refractory Metals and Hard Materials, 2001, 19, 293-301. [14] Chai H., Lawn B.R., A universal relationship for edge chipping from sharp contacts in brittle materials: A simple means of toughness evaluation, Acta Materiala 2007, 55, 2555-2561. [15] Quinn J., Su L., Flanders L., Lloyd I., “Edge toughness” and material properties related to the machining of dental ceramics, Machining Science and Technology, 2000, 4, 291-304.

ACCEPTED MANUSCRIPT [16] Petit F., Vandeneede V., Cambier F., Ceramic toughness assessment through edge chipping measurements-Influence of interfacial friction, Journal of the European Ceramic Society, 2009, 29, 2135-2141. [17] Felten F., Schneider G.A., Sadowski T., Estimation of R-curve in WC/Co cermet by CT test, International Journal of Refractory Metals & Hard Materials, 2008, 26, 55–60.

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[18] Patle V., Bhadauria S.S., Jain A., Analysis of Crack Tip Opening Displacement under Mixed Mode Fracture Using FEM Technique, IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE), 2012, 3, 27-34.

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[19] Fischmeister H.F., Schmauder S., Sigl L.S., "Finite Element Modelling of Crack Propagation in WC-Co Hard Metals, Materials Science and Engineering, 1988, A105/106, 305-311. [20] Gomes M.A., Wronski A.S., Monotonic subcritical crack growth in T42 high speed steel, International Journal of Fracture, 1997, 83, 207–221.

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[21] Saveker J., Composite cutting tools, wear resistant bodies and finished products, Patent WO 2007029017 A1, 15 March 2007. . [22] Krishtal M.A., Turkel'taub G.M., Microstructure of iron-boron alloys, Metal Science and Heat Treatment, 1967, 9, 620-621.

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[23] McClintock F.A., Irwin G.R., Plasticity aspects of fracture mechanics, ASTM STP 381, Fracture toughness testing and its applications, 1965, 84-113.

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[24] Johannesson B., The fracture behaviour of hardmetals- with particular reference to temperature, PhD thesis, Chalmers University of Technology, Gőteborg, 1987.

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[25] Shetty D.K., Wright I.G., Mincer, P.N., Clauer, A.H., Indentation fracture of WC-Co cermets, Journal of Materials Science 1985, 20, 1873-1882.

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[26] Warren R., and Matzke H.J., Indentation testing of a broad range of cemented carbides, Proc 1st Int Conf. on Science of Hard Materials, eds. Viswanadham, Rowcliffe and Gurland, Plenum Press, New York, 1981, 563-582. . [27] Exner H.E, Pickens J., and Gurland J, A comparison of indentation crack resistance and fracture toughness of WC-Co alloys, Metallurgical Transactions A, 1978, 9, 736. [28] Wright B.D., Green P.J., Braidenp.n., Quantitative analysis of delayed fracture observed in stress rate tests on brittle materials, Journal of Materials Science 1982, 17, 3227-3234. [29] Lawn B.R., Fracture of brittle solids, 2nd. Ed., Cambridge University Press, Cambridge 1993.

ACCEPTED MANUSCRIPT [30] Torres Y., Casellas D., Anglada M., Llanes L., Fracture toughness evaluation of hardmetals: Influence of testing procedure, International Journal of Refractory Metals and Hard Materials 2001, 19, 27-34. [31] Irwin, G. R., Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate, Journal of Applied Mechanics 1957, 24, 361-364.

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[32] Quinn G.D. and Quinn J.B., A New Analysis of the Edge Chipping Resistance of Brittle Materials, Mechanical Properties and Performance of Engineering Ceramics and Composites IX (eds. Singh D. and Salem J.), The American Ceramic Society 2015.

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[33] Swanson G.D., Fracture energies of ceramics, Journal of the American Ceramic Society, 1972, 255, 48-49.

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[34] Gogotsi, G., Mudrik S., Galenko V., Evaluation of fracture resistance of ceramics: Edge fracture tests, Ceramics International 2007, 33, 315-320.

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[35] Gogotsi, G., Fracture behaviour of Mg-PSZ ceramics: Comparative estimates, Ceramics International 2009, 35, 2735-2740.

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[36] Choi, S.R., Salem, J.A., Cyclic fatigue of brittle materials with an indentationinduced flaw system, Materials Science and Engineering, 1988, A208, 126-130.

ACCEPTED MANUSCRIPT Edge Toughness of Tungsten Carbide Based Hardmetals

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Highlights: Resistance to edge fracture of a group of WC-based hardmetals is reported. The edge fracture parameter is compared to more conventional plane strain KIC and also to Palmqvist toughness. Statistics from the test are also studied in detail to try to establish how many edge fracture events in a given material are needed to provide credible variance.