Computational Materials Science 83 (2014) 434–442

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Computational Materials Science

journal homepage: www.elsevier .com/locate /commatsci

Microstructure-level modeling and simulation of the flexural behaviorof ceramic tool materials

0927-0256/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.commatsci.2013.11.049

⇑ Corresponding author. Tel./fax: +86 531 88393904.E-mail address: zhaojun@sdu.edu.cn (J. Zhao).

Dong Wang, Jun Zhao ⇑, Jiabang Zhao, Anhai Li, Xiaoxiao ChenKey Laboratory of High Efficiency and Clean Mechanical Manufacture of MOE, School of Mechanical Engineering, Shandong University, 17923 Jingshi Road, Jinan 250061, PR China

a r t i c l e i n f o

Article history:Received 13 August 2013Received in revised form 20 November 2013Accepted 25 November 2013Available online 15 December 2013

Keywords:VoronoiMicrostructure modelFlexural behaviorNumerical simulationCeramic

a b s t r a c t

The flexural behavior of ceramic tool materials is investigated by both experiments and numerical sim-ulation. The Voronoi Tessellation hybrid random algorithms are utilized to construct a microstructuremodel to simulate the flexural behavior of ceramic. The secondary phase volume fraction, the nano-scaleparticle volume fraction, the grain centroid distribution, and the grain diameter distribution of the mate-rials are considered in the model. The flexural strength of ceramic materials is calculated via the simula-tion of three-point bending tests. The effects of average grain diameter, nano-scale particle and secondaryphase volume fraction on the flexural strength of ceramic materials are systematically studied. Thenumerical simulation results show good agreement with the experimental results.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Ceramic materials possess a series of excellent properties whichare indispensible for tool materials, such as high hardness, greatwear resistance, good chemical stability and heat resistance [1,2].Whereas, one of the intrinsic drawbacks of ceramic cutting toolsis relatively low flexural strength and fracture toughness, whichusually makes them more susceptible to excessive chipping orfracture when machining hardened materials [3]. During the pasttwo decades, much effort has been made to improve the strengthand toughness of ceramic materials. Several useful methods havebeen proposed, such as dispersion of different particles in a matrix,fiber or whisker reinforced composites and micro-nano reinforcedcomposites [4–8].

Recently, grain size effects on mechanical properties of compos-ite ceramics were widely studied [9–11]. The effects of Al2O3 par-ticle size on the mechanical properties of alumina-based ceramicswere investigated by Teng et al. [9]. The effect of starting powdersize on Al2O3/TiC composites were studied by Liu et al. [11]. Con-ventionally, Al2O3-based ceramic tool materials were strengthenedby the addition of micro-sized particles like TiC, TiN, ZrO2, (W, Ti)C,TiB2, etc. or SiC whisker to improve the mechanical properties [12–15]. Formerly, many studies have been carried out to evaluate theeffect of addition of secondary phase on the microstructure andmechanical properties of ceramic. The effect of addition of TiC onthe mechanical properties of Al2O3 based composites were exam-

ined by Cai et al. [12]. The effect of (W, Ti)C content on the micro-structure and mechanical properties of B4C/(W, Ti)C ceramiccomposites were studied by Deng et al. [14]. Since, Niilhara firstlyreported that the addition of nano-particles to the Al2O3 matrixcould improve mechanical properties notablely, especially the re-searches on nano Al2O3-based composites were conspicuouslydeveloped [16]. The investigation on preparation ceramic compos-ites for cutting tools by adding nano-scale particle, such as TiC,Al2O3 and TiN, to the Al2O3 matrix have drawn more attention[17–19]. Davidge et al. [17] showed a clear evidence for significantstrengthening and toughening due to the addition of approxi-mately 100 nm SiC particles to Al2O3.

Microstructure plays an important role in determining themechanical properties of ceramic tool materials [20]. The mechanicalproperties would be affected by grain diameter, grain distribution,grain shape and constituent phases [21,22]. It is difficult to quan-tify the correlation between microstructure and materials proper-ties due to the complexity of ceramic microstructure. Recentlymany numerical and theoretical models have been developed toreveal this correlation [23–25]. Sukumar and Srolovitz [23] simu-lated the crack propagation of polycrystalline materials by themeans of X-FEM. A simulation of crack propagation in microstruc-ture of ceramic was presented by Wang et al. [24]. The effects ofrandomness in the distribution of microstructure parameters havebeen generally neglected or scarcely considered in these simula-tion models. To this end, the objective of this paper is to developa microstructure-level model to simulate the flexural behavior ofceramic material. The model was based on the Voronoi Tessellationin which random algorithm was employed by taking into account

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the secondary phase volume fraction, nano-scale particle volumefraction, the grain centroid distribution and the grain diameter dis-tribution of the materials.

In this paper, a type of Al2O3-based composite ceramic toolmaterial simultaneously reinforced with micro-scale (W, Ti)C andnano-scale Al2O3 particles is fabricated by using hot-pressing tech-nology, the experimental procedures and results are described inSection 2. Then, a microstructure model is developed by usingVoronoi Tessellation and random algorithm. The detailed construc-tion of microstructure model and the simulation procedures arepresented in Section 3. The simulated results and discussion are gi-ven in Section 4. Eventually, some concluding remarks obtainedfrom this study are given in Section 5.

2. Experimental procedures

2.1. Materials preparation

The starting materials are a-Al2O3 powders with average grainsize of approximately 0.5 lm (purity: 99.99%, Shanghai, China),nano-scale Al2O3 with an average particle size of approximately140 nm (purity: 99.9%, Zibo, China) and (W, Ti)C with an averageparticle size of 1 lm (purity: 99.99%, Hefei, China). Nine differentcomposition rations are tested as shown in Table 1. The nano-scale Al2O3 powders are prepared into suspensions using alcoholas the dispersing medium, and the dispersant PEG (polyethyleneglycol, Shanghai, China) is added after ultrasonic dispersion (withSB5200 ultrasonic instrument and D-7401-III motor stirrer, China)for 10 min. The suspensions are dispersed ultrasonically for20 min after a pH of 9.0 (with PHS-25 digimatic pH-meter, China)is attained by the addition of NH3�H2O. After the nano-scale Al2O3

particle suspension is dispersed well, they are then mixed withmicro Al2O3, micro (W, Ti)C. MgO and NiO (Shanghai, China) areused as sintering additives to promote the densification of thecompacts and retard the grain growth of Al2O3 matrix duringthe sintering process. The mixed slurries are ball-milled for48 h, and then dried in a vacuum dry-type evaporator (ModerZK-82 A, China). After that, the dried powders are sieved througha 200-mech sieve for further use. The dried powders are placedinto a graphite die and hot-pressed with an applied pressure of32 MPa at 1650 �C with the holding time of 20 min in vacuumin a sintering furnace.

2.2. Characterization

Each sintered compact (with 42 mm diameter) is cut andmachined into five bend bars with the dimension of3 mm � 4 mm � 20 mm and then ground flat to a 10 lm finish.Flexural strength is measured using a three-point bending tester(Model WD-10, China) with a span of 20 mm and a loading velocityof 0.5 mm/min. The flexural strength for the nine composites is

Table 1Composition (vol.%) and flexural strength of different composites.

Composites Micro-scaleAl2O3 (0.5 lm)

(W, Ti)C(1 lm)

Nano-scaleAl2O3

(0.14 lm)

Flexuralstrength, rf

(MPa)

AW15 85 15 0 531.27AW25 75 25 0 723.40AW35 65 35 0 781.12AW45 55 45 0 796.95AW55 45 55 0 580.65W45N5 50 45 5 817.33W45N10 45 45 10 832.52W45N15 40 45 15 819.51W45N20 35 45 20 810.83

given in Table 1. The fracture surfaces are observed by scanningelectron microscopy (SEM, SUPRA-55, ZEISS, Germany).

3. Numerical simulation procedures

3.1. Microstructure modeling of ceramic materials

Voronoi diagram (VD) is a kind of important geometric struc-ture in Laguerre geometry. The space is divided into many regionsin accordance with the shortest property of element in the set ofobjects (points or lines). The ceramic grain matrix is similar tothe Voronoi cells in the shape. The matrix microstructure modelis constructed by using of the VD in this paper. Some basic micro-structure parameters of ceramic, including average diameter andcentroid, are considered in the model. The incremental method isused to construct the VD based on hybrid programming of MATLABand VC++. In the algorithm of incremental method, the new seedpoints are added gradually into the VD which has been constructedwith seed points. There are two main steps to establish the model[24]. Firstly, the location of newly added seed point pk+1 is checkedin the VD (pk). VRp (pi) indicates the cell of seed point pi in the VD.In Fig. 1(a), the location of pk+1 could be determined by comparingthe distance between pk+1 and the point in the set Pk = {p1,p2, . . .

,pk}. Once the point pi with the minimum distance away fromthe pk+1 is determined, the fact that the pk+1 located in the VRp

(pi) could be found. Then, the Voronoi cell VRp (pk+1) is producedby the point with minimum distance away from the pk+1. The dot-ted line indicates the VRp (pk+1) in Fig. 1(a). VRp (pi) is separatedinto two parts by the straight bisector between pk+1 and pi. Thereare two intersection points (q and t) in the boundary of VRp (pi).The intersection points (t and n) are found in the adjacent cellVRp (pj) by using the same method. The process would be accom-plished until a polygon appeared. Finally, the new cell VRp (pk+1)is generated by deleting the boundary and vertex in that polygon.The new Voronoi cell in Fig. 1(b) is developed.

The simulation of ceramic microstructure starts with the gener-ation of cell points. A set of cell points are generated by using theuniform distribution function based on the MATLAB. Then the cellpoints are inserted into the matrix one by one. With the addition ofthe cell points, the new VD is constructed correspondingly. Theprocess is terminated until the grain diameter reaches a designatedvalue. Then, the convex quadrilaterals are put into the matrix ran-domly to simulate the secondary phase (see Fig. 1(c)). The locationof quadrilateral is determined by the uniform distribution function.In this process, it is inevitable that there are overlapping cells,which can be removed by a series of Boolean operations (seeFig. 1(d)). The total areas of added quadrilaterals are calculatedwith the adding process. The program would ceases to run whenthe area reach a designated value. After this step, the ceramicmicrostructure with secondary phase is constructed. In Fig. 2(a),the light-colored cells and the deep-colored cells indicate theAl2O3 matrix and the secondary phase of (W, Ti) C, respectively.In order to simulate the nano-scale particle Al2O3, dots with certaindiameter are randomly added into the above generated model. Thenumber of circles is determined by the volume fraction of nano-scale Al2O3. The microstructure model with nano-scale particle isshown in Fig. 2(b) in which the dots are the nano-scale particleAl2O3.

Table 2Material parameters of microstructure.

Material q (kg/m3) E (GPa) m

Al2O3 3990 374 0.22(Ti, W)C 9490 570 0.2

Fig. 1. Construction process of ceramic model based on VD and random algorithm. (a) Location of pk+1 and generation of VRp (pk+1). (b) Construction of new VD. (c) Addition ofquadrilaterals into matrix. (d) Processing for overlapped area.

Fig. 2. Generated microstructure of the ceramic. (a) With secondary phase. (b) With nano-scale particle.

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3.2. Simulation procedures

In order to investigate the effects of microstructure features onthe flexural behavior of Al2O3/(W, Ti)C ceramic materials, the pro-cess of three-point bending test is simulated by using the micro-structure model obtained above. The Abaqus software is appliedto simulate the three-point bending test. The simulation of flexuralbehavior of ceramic materials is carried out with regard to differ-ent microstructure models with various microstructure features.The main microstructure features are considered in the simulation,including average grain diameter, secondary phase volume fractionand nano-scale particle volume fraction.

A three-point bending specimen in plain strain, subjected tovelocity loading, is considered. Fig. 3 shows the schematic of thethree-point bending specimen. The length of the model is 20 lm,and its height is 3 lm. A four-node bilinear plane stress quadrilateral

element is used for the Abaqus/Standard analysis. The bottom andtop edges of model are traction free. The compressive behavior ofceramic in the cracking model in Abaqus/Explicit is assumed tobe linear elastic. Under this assumption, crack propagation ismainly promoted by the tension in the bending specimen. Table 2shows the material parameters of microstructure models. The brit-tle cracking criterion is applied in the computational procedure forgrains in the microstructure of ceramic. A type of GFI (Mode I frac-ture energy) is selected as the brittle cracking criterion. A velocityof 0.01 mm/s is applied on the center of specimen.

In order to investigate the effect of microstructure parameterson the mechanical response, different models with various param-eters are established. The microstructure parameters of variousmodels are described in Table 3. Microstructure models a-m con-structed to simulate the flexural behavior of ceramic is shown inFig. 4.

Fig. 3. Schematic of the three-point bending specimen.

Table 3Parameters of microstructure models.

Composites Average graindiameter (lm)

Secondary phasevolume fraction (%)

Nano-scale Al2O3

volume fraction (%)

A 0.5 45 10B 0.75 45 10C 1 45 10D 1.25 45 10E 1.5 45 10F 0.5 15 0G 0.5 25 0H 0.5 35 0I 0.5 45 0J 0.5 55 0K 0.5 45 5L 0.5 45 15M 0.5 45 20

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3.3. The calculation of the flexural strength

The load–displacement curve could be obtained after the simu-lation of three-point bending test. The flexural strength is calcu-lated by using the definition of flexural strength in the classicelastic–plastic mechanics based on the experiment (see Eq. (1)).

rf ¼3PL

2bh2 ð1Þ

where rf is the flexural strength of material, P is the load, L, b and hare the length, width and height of the specimen, respectively. Thevalue of width in this paper is supposed 1 lm.

4. Results and discussion

4.1. Results

The flexural behavior simulation results of microstructuremodels are shown in Fig. 4. It can be seen that the crack modesof ceramic materials with various microstructure parameters areintergranular crack and transgranular crack. SEM micrograph offracture surfaces of ceramic materials is shown in Fig. 5. As isshown in the figures, the crack mode of ceramic materials is amixture of intergranular and transgranular types. It is concludedthat the simulated results reflect the fracture modes of thecracks.

4.2. Effect of average grain diameter on the flexural strength

Grain diameter is an important factor of microstructure param-eters for ceramic materials. It is mainly determined by powderparticle sizes, powder ingredients and sintering conditions. Manystudies have indicated that the flexural strength of ceramic isclosely related with grain diameters.

Composites A, B, C, D and E have same microstructureparameters but different grain average diameters, which are0.5, 0.75, 1, 1.25, and 1.5 lm, respectively. So the effect of graindiameters on flexural strength can be represented in Fig. 4(a–e).For composite A (shown in Fig. 4(a)), the crack modes areintergranular crack and transgranular crack. As to composite E(shown in Fig. 4(e)), only the transgranular crack could befounded in the simulation results. The result indicates that thepossibility of the generation of the intergranular crackincreases with the decreasing grain diameter. The intergranularcrack is useful for improving the flexural strength of ceramicmaterials.

Fig. 6 shows the applied force versus displacement for compos-ites (A, B, C, D, and E). It can be seen that the applied force at com-posite A shows a little greater than the other four models. Thisillustrates that the applied force increases with the decrement ofthe average grain diameter of the composites.

Fig. 7 illustrates the flexural strength versus averagegrain diameter of composites. With the increase in averagegrain diameter, the flexural strength became smaller. Becausethe applied force at composite A is much higher than that fourcomposites B, C, D and E. The flexural strength of composite Ais 868.6 MPa, and that of B, C, D and E are 849.3, 784.2, 728.5,and 603.2 MPa, respectively. Compared with composite B, C, Dand E, the applied force at composite A reaches high value toform a crack, therefore high strength will be obtained in thiscomposite. This is consistent with the experimental phenomenathat more fine grains normally possess higher flexural strengththan comparable ceramic materials with coarse grains. It is pos-sible to obtain excellent ceramic materials with high flexuralstrength by refining the grain diameters.

4.3. Effect of second phase volume fraction on the flexural strength

The brittleness of single phase Al2O3 ceramic limits its applica-tion as cutting tools. Some researchers proposed many methods toimprove the strength of ceramic, including nano-compositestrengthening, self-reinforced, transformation toughening and par-ticle strengthening. The method of particle strengthening could im-prove the toughness and strength of material. At the same time, it isthe most effective and easiest way to improve the strength of cera-mic. In this paper, the ceramic with the secondary phase of (Ti,W)C is investigated.

Various secondary phase volume fractions are changed in com-posites F, G, H, I and J which are 15%, 25%, 35%, 45%, and 55%,respectively. The other microstructure parameters adopted inthose models are identical with each other. The effect of secondaryphase volume fractions on flexural strength is illustrated inFig. 4(f–j). The intergranular and transgranular crack can befounded in the composite I (shown in Fig. 4(i)). There is only thetransgranular crack can be obtained in the composite f (shown inFig. 4(f)). The result indicates that the possibility of the generationof the intergranular crack increases with the secondary phase vol-ume fraction.

The applied force versus the displacement for composites F,G, H, I and J are illustrated in Fig. 8. It can be indicated thatfirstly the applied force at composites increases, and thendecreases with increasing the secondary phase volumefraction. When the volume fraction of secondary phaseadded is 45%, the applied force is the highest for thecomposites.

Fig. 9 shows the effect of secondary phase volume fraction onthe flexural strength of ceramic microstructure. It is demonstratedthat the flexural strength reaches a maximum value at 832.4 MPawhen secondary phase volume fraction reaches 45%. Firstly the

Fig. 4. Flexural behavior simulation results of the corresponding microstructure models. (a) Composite A; (b) composite B; (c) composite C; (d) composite D; (e) composite E;(f) composite F; (g) composite G; (h) composite H; (i) composite I; (j) composite J; (k) composite K; (l) composite L; (m) composite M.

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flexural strength increases, and then decreases with the increasingsecond phase volume fraction. The values of flexural strength ofcomposites F, G, H, I and J are 562.3, 750.5, 789.5, 832.4 and601.2 MPa, respectively. It could be proved that the second phase

particle (Ti, W)C could improve the toughness of ceramic. Hence,excellent Al2O3 ceramic with the higher flexural strength couldbe obtained by adding the second phase particle (Ti, W) C in thematerial.

Fig. 4 (continued)

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4.4. Effect of nano-scale particle volume fraction on the flexuralstrength

The effect of nanoparticles on alumina matrix was first demon-strated by Niihara [16] who reported that the flexural strength and

fracture toughness of monolithic alumina were increased with 5%SiC nanoparticles. Niihara proposed that strength was improveddue to the refinement of microstructural scale which was fromthe order of the alumina grain size to the order of interparticlesspacing, thus reducing the critical flaw size.

Fig. 4 (continued)

Fig. 5. SEM micrograph of fracture surface of ceramic materials. (a) AW45; (b) AW45N5.

440 D. Wang et al. / Computational Materials Science 83 (2014) 434–442

In order to investigate the effect of nano-scale Al2O3 volumefraction on the flexural strength of ceramic materials, five mod-els with different nano-scale Al2O3 volume fraction are utilizedin this study. As it is demonstrated in Table 3, the nano-scaleAl2O3 volume fractions of composites I, K, A, L and M are 0%,5%, 10%, 15%, and 20%, respectively. The other microstructureparameters in these models are same with each other. The effectof nano-scale Al2O3 volume fraction on flexural strength is illus-trated in Fig. 4(i), (k), (a), (l) and (m).

Fig. 10 shows the applied force at the composites I, K, A, L andM. It is clearly concluded that firstly the applied force increases,

and then decreases with increasing the nano-scale Al2O3 volumefraction. When the volume fraction of nano-scale phase isadded to 10%, the applied force reaches the highest for thecomposites.

The flexural strength for the different nano-scale phase volumefraction is presented in Fig. 11. It could be observed that flexuralstrength firstly increases, and then decreases with the incrementof nano-scale phase volume fraction. For composite A, the valueof flexural strength reaches 868.6 MPa, while for composites I, K,L, and M the flexural strength are 832.4, 841.2, 834.8, and825.3 MPa, respectively. It can be concluded that the optimum

Fig. 6. Variations of force applied to microstructure model with the average graindiameters.

Fig. 7. Variations of flexural strength of microstructure model with the averagegrain diameters.

Fig. 8. Variations of force applied to microstructure model with the secondaryphase volume fractions.

Fig. 9. Variations of flexural strength of microstructure model with the secondaryphase volume fractions.

Fig. 10. Variations of force applied to microstructure model with the nano-scalephase volume fractions.

Fig. 11. Variations of flexural strength of microstructure model with the nano-scalephase volume fractions.

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content of the nano-scale phase is beneficial for increasing the frac-ture toughness of ceramic materials.

5. Conclusion

A microstructure model was developed to simulate the flexuralbehavior of ceramic materials. The model is introduced with spe-cial consideration of the average grain diameter distribution, thegrain centroid distribution, the secondary phase volume fractionand the nano-scale phase volume fraction based on Voronoi Tessel-lation and the random algorithm.

The flexural behavior of ceramic materials is simulated byemploying ABAQUS code with a brittle cracking criterion. It couldbe seen that the intergranular and transgranular crack are the frac-ture modes of ceramic materials. The simulation results shows thatthe intergranular crack could be promoted by adding the second-ary phase (W, Ti) C. The added nano-scale phase can lead to crackdeflection.

The flexural strength of materials is obtained based on simula-tion results. The effects of average grain diameter, secondary phasevolume fraction and nano-scale phase volume fraction on the flex-ural strength of ceramic are investigated. It could be concludedthat average grain diameter significantly affects the flexuralstrength. The flexural strength increases with the decrement ofaverage grain diameters. It is also noteworthy that the secondaryphase (W, Ti) C and nano-scale phase could improve the flexuralstrength of ceramic materials.

Acknowledgements

This work is sponsored by the National Basic Research Programof China (2009CB724402) and the National Natural Science Foun-dation of China (51175310).

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