FRACTURAL PROCESS AND TOUGHENING MECHANISM OF LAMINATED CERAMIC COMPOSITES

Acta Mechanica Solida Sinica, Vol. 20, No.2, June, 2007ISSN 0894-9166Published by AMSS Press, Wuhan, China. DOI: 10.1007/s10338-007-0717-xFRACTURAL PROCESS AND TOUGHENINGMECHA NISM OF LA MINATED CERA MICCOMPOSITES **Zhang Yafangl*( Faculty of Civil Engineering, Guangzhou University, Guangzhou 510006, China)Tang Chun'an2Zhang Yongbin3 Liang Zhenzao2(2 School of Ciwil and Hydraulic Engineering, Dalian University of Technology, Dalian 116024, China)(3 Research Center for Numerical Test on Material Failure, Dalian University, Dalian 116622, China)Received 9 December 2006; revision received 13 June 2007.ABSTRACT Based on the model of multi-layer beam and the assumption of micro-inhomogeneityof material, the 3D fractural characteristics of laminated ceramic composites have been studiedwith numerical simulation. U nder three-point bending load, crack initiation, coalescence, propa-gation, tuning off in the weak interface and final rupture have been simulated. The spatial distri-bution and evolution process of acoustic emission are also presented in the paper. The simulationverifies the primary mechanism of the weak interface inducing the crack to expand along there andabsorbing the fractural energy. The disciplinary significance of the effect of strength and prop-erties of material on the toughness and strength of laminated ceramic composites is, therefore,discussed in this paper.KEY WORDS laminated ceramic composite, toughening, numerical simulationI. INTRODUCTIONCeramic composites are now widely applied in aeronautical and space engineering, metallurgy, civilengineering and automotive manufacturing due to the advantages such as high strength, high stifness,good endurance of high temperature and corrosion, etc. However, the most critical obstructs on suchapplications is brittleness. How to strengthen and toughen the ceramic composite is a hot topic in recentyears.Soft layers are combined with ceramic's brittle structure, so the laminated ceramic composites couldbe treated as a bionice structure, similar to that of shelves and bones in nature. Traditionally, the ap-proaches to improving toughness could be simply summarized as faults elimination. However, tougheningmechanism of the laminated ceramic is different and particular. Since Clegg et al.l1] published theirwork in 'Nature，many studies have been carried out in material preparation, fractural characteristics,mechanical characteristics and toughening mechanism in this field2- 5].In these studies, some researchers, like ChanglO] and Guol7 tried to apply numerical methods tothis field. Up to date, however, most of these studies were two- dimensional ones. If a three-dimensional★Corresponding author. E-mail: zhangyafang2004@ 163.comsponan** Funding by: S&T Project No.2006B14601004, Guangdong Province; S&T Project No.62047, Educational Bureau,Guanzhou City and Fund of Natural Science, Guangdong Province (No.05001885).中国煤化工MHCNM HGACTA MECHANICA SOLIDA SINICA2007model could be developed, the spatial distribution of crack initiation, coalescence, propagation, andthus a real fractural process in composite could be studied, which is of great importance and significancefor understanding of the mechanism of the fractural process and toughening of composite ceramics.II. NUMERICAL MODELINGscale. Thus the heterogeneity of material is essential to model verification. Compared to the traditionalnumerical method, where laminated composite ceramic is usually treated as homogeneous material bymany researchers, great improvement has been made with a code named RFPA3D (3D Realistic FailureThe ceramic matrix here is divided into cells of a hexahedron, and the heterogeneity of mechanicalfeatures is represented with a two parameters Weibull distribution. The probability distribution functioncan be described as follows:f(a)="(9).e-(a/ao)where a stands for mechanical characteristic parameters, such as Young's modulus, strength, the Pois-son's ratio, etc. ao is the mean value of a, m is the shape factor of Weibull, defined as the homogeneityindex of material.The choice of a proper fracture criterion is crucial to cracking simulation. A Coulomb criterion[8]envelope with a tensile cut-off is adopted in this paper for brittle materials. The tensile failure will occurwhen the principal stress in an element is greater than its tensile strength, see formula (2). Meanwhile,to simulate the shear failure, the second valve criterion as formula (3) is also used.σ1≥σt(2)and/or.1+sinφ1- sinσ1-σ3≥σcwhere φ is the frictional angle, σ1 and σ3 are the maximum and minimum principal stresses, respectively,σt and σc are the uniaxial tensile and compression strength of an element, respectively.After a displacement vector is applied to the model, stress and deformation in each element are thencomputed. When the fracture criterion is met in an element, the element is considered to be weak orfailed. The failed element has been applied a very low elastic modulus instead of being removed from themesh. The stress and the deformation distribution throughout the model are adjusted instantaneouslyafter each element ruptures in an equilibrium state. In the areas with increased stress due to stressredistribution, the stress may exceed the critical value so that further ruptures will occur. The processwould be repeated until no more elements exceed the fracture criterion under the same load. Then, thecalculation would move to the next step by a small increment and the procedure can be repeated untilthe whole specimen fractures.In this calculation, the stress and strain can be obtained by introducing a damage factor D.(4)e=E=(1-D)Eosoft layersFig. 1. Three-dimensional numerical model of laminated (中国煤化工YHCNM HGVol. 20, No. 2 Zhang Yafang et al: Fractural Process and Toughening Mechanism of Composites143.and/orσ= Eo(1- D)e(5)where Eo and E are Young's moduli for the initial stage and damaged stage, respectively.For damage factor D, when no damage happens in the cell, D = 0, and when the cell is completelydamaged, D = 1. Corresponding to a given damage status, D is in the range of0and1,ie.0< D< 1.The beam model under the three-point bending load adopted in this paper is presented in Fig.1. An .ideal interface is applied between the soft and the hard layers to ignore the effect of the real interface.The beam with dimensions of 50 x 250 x 30 mm comprises a total number of 50 x 250 x 30 = 375000cells. A notch with dimensions of5 X 2 x 30 mm is in the central bottom of the beam. For each softand hard layer, the ratios to the thickness, Young's modulus, and the strength are 1 : 10, 1 : 10 and1 : 8, respectively. This calculation was completed on a parallel computer system.III. THE FRACTURAL PROCESS AND TOUGHENING MECHANISMThe load-displacement curve of a laminated ceramic is presented in Fig.2, comparing a curve of a300- blocklaminatedceramic block. From the figure, the strength of the250materiallaminated ceramic is higher than that of the ceramic200block. Simultaneously, the fractural work increases15122%. Here the fractural work K is defined as the100area the load-displacement curve envelopes divided5(by the cross section of the beaml9]. An explanation of05 50 100 150200 250 300 350 400 450 500 550 .such a phenomenon can be obtained from the failuredisplaceneant (x1.0E-3mm)process of the specimen, which will be discussed inthe following text.Fig. 2 Load-displacement curves of laminated ceramic.tip of the notch. The micro cracks will initiate near this tip due to the stress concentration. With anincrease in the load, the crack will coalesce in this area and propagate upwards until the upper boundaryof the beam is reached. Figure 2 also shows that for the block the curve has only one peak point whichillustrates that the fracture is a one-off event; and the development of the crack is rapid while theresidual stress is small.The fractural process of laminated ceramic specimen is presented in Fig.3 through the images ofmodulus and maximum principal stress. From Fig.3(a), i.e. the modulus images, it can be found thatthe crack propagates upwards first and then deflects into the soft layer when the soft- hard interface ismet. After that the crack develops horizontally within the soft layer. With the increase of the load, thecrack turns back and develops vertically again. This procedure is repeated at each soft layer , so verticaland horizontal cracks appear alternately until the beam finally fractures. As a result, the fracture is nolonger a rapid process but a layer by layer one.Moreover, from Fig.3(b), the maximum principal stress images, the crack appears first near the tipof the notch due to stress concentration. Then the main crack develops upwards. When the first softlayer is met, a 3D stress field is changed to a 2D field10,11]. A‘dummy plastic zone' appears near thetip of crack and a so-called passivation will release the stress concentration in this zone, as a result thevertical trend of the cracking is restrained and the crack develops horizontally. In this procedure, thesoft layer acts as a shield.After the crack traverses at a distance within the soft layer, some new vertical cracks appear withthe increase of the load. As more energy is needed for this crack initiation, the strength of laminatedceramic is in general higher than that of the ceramic block. Figure 3 also illustrates that the crack isno longer a straight line but in a zigzag shape or a brick shape. This phenomenon is also observed inthe description of a similar test by Guol12]. The conclusion drawn in this section is also in agreementwith the laboratory tests carried out by Cail13] and Tan[14Images of acoustic emission (AE) for both block and laminated ceramic are presented in Fig.4, wherea circle represents an AE event. The radius is directly proportional to the energy dissipated from thedamaged cell. For the ceramic block, Fig.4(a) shows that most AE events are located in a narrow beltdeveloping along the load direction, and almost no horizontal events present. This ilstrates that. cracks中国煤化工MHCNM HGACTA MECHANICA SOLIDA SINICA2007elastic modulus (MPa) step 12-()max principal stress (MPa) step 12-(0)elastic modulus (MPa) step 16-0)max principal stress (MPa) step 16-(0)elastic modulus (MPa) step 26-(0)max principal stress (MPa) step 26-(0)elastic modulus (MPa) step 30-(0)max principal stress (MPa) step 30-(0)elastic modulus (MPa) step 46-(0)max principal stress (MPa) step 46-(0)(a) modulus(b) max principal stressFig. 3. Fractural processes of laminated model.in this block do not propagate horizontally. On the other hand, from Fig.4(b), though most AE eventsoccur along the vertical direction, more AE events could be found in the horizontal one. It is quiteclear that most horizontal AE events are located within soft layers. In addition, the radii of AE eventsshown in Fig.4(a) do not change rapidly from the area near the bottom of the beam to the upper part.This shows that the energy dissipated from each cells in the fracture belt is almost at the same level.But it can be seen from Fig.4(b) that the energy dissipated from the vertical cracks is much greaterthan that in the horizontal direction. The same conclusion can also be obtained from Ref.[15] in the2D condition.中国煤化工MHCNM HGVol.20, No. 2 Zhang Yafang et al: Fractural Process and Toughening Mechanism of Composites145Y__Y2东acoustic emission step 40-(0)xacoustic emission step 46-(0)|x(a) ceramic block structure(b) laminated composite ccramieFig. 4. Numerical simulation of AE in laminated model.IV. THE EFFECT OF STRENGTH OF SOFT LAYERSTo investigate the effect of strength of soft layers using the same beam models presented in theprevious section (Fig.1), numerical simulation on a group of eight specimens with different strengthsof the soft layer has been conducted. The strength ratios of soft layers to hard layers are set to be 0.12,0.16, 0.2, 0.24, 0.28, 0.32, 0.36 and 0.4 for each specimen, while other features remain unchanged.The results of the simulation are presented in Fig.5, where the curves of fractural work K and thepeak load versus strength ratio are plotted as Fig.5(a) and 5(b), respectively. From these figures, itis clear that the fractural work K and the peak load P decrease while the strength of the soft layersincreases. In particular, when the strength ratio is in the range 0.24-0.28, both K and P decrease rapidly.This implies that if the strength of the soft layer is very high, the deflection and the softening of thecrack tips can hardly happen. Meanwhile, if the strength of the soft layer is very low, it will not beadvisable to improve the mechanical characteristics of the composite ceramic. In fact, a specimen withstrength ratio of 0.08 is also tested, and it is found that all the fractures occur along the soft layer, sothat no crack initiates or propagates vertically.50 |2050|三300280 t这40三30|24020|2020.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44strength ratio of soft and hard layers(a) fracturul work K(b) peak loaed PFig. 5. Curves of fracture energy and peak load of the laminated models versus the strength of soft layer.The explanation about this efect can be deduced from Fig.6, where the fractural process is presentedfor each specimen. For the specimens No.1 to 4 with relatively low strength soft layers, an obvious crackdeflection can be observed. First the cracks initiate near the tip of the notch, and then propagatevertically along the load direction. Passivation on the crack tips happens when a soft layer is met andthe crack defects along the horizontal direction, i.e. along the soft layer. The lower the strength of thesoft layer is, the longer distance the crack goes over horizontally and more energy is dissipated in thecracking process. On the other hand, for the specimens No.5 to 8 with relatively high strength softlayers, the cracks develop upwards quickly but over a shorter distance horizontally. Compared with thecases in previous specimens, less deflection happens and less energy is dissipated. So the tougheningeffect is not manifest and the laminated ceramic has nearly similar fractural work K as the ceramicblock, i.e., no critical improvement has been made on the toughness of the ceramic.Based on the previous discussion, the strength of the soft layers is crucial to the attempt at improvingthe toughness of the laminated ceramic material. Only those soft layers of adeouatestrenoth can inerease中国煤化工MYHCNM HG146.ACTA MECHANICA SOLIDA SINICA2007the fractural work K , make the crack deflected and more energy dissipated and, therefore, reduce thebrittleness of the material. The numerical simulation is in excellent agreement with the laboratory testscarried out by Cai13) and Tanl14]. The results from 2D numerical simulation performed by Chang0do not conflict with the present ones.The approaches adopted in this study can also be applied to other materials with laminated structure.As a matter of fact, several toughening mechanisms may work together, however, the energy dissipationdiscussed in this section is the primary one.z之elastic modulus (MPa) step 128-(0)acoustie emision step 128-(0)specimen 12elastic modulus (MPa) step 99-(0)acoustie emission step 99-(0)speimen 2elastic modulus (MPa) step 96-(0)acoustice erision step 96-()xspecimen3elastic modulus (MPa) step 98-(0)acoustie cmission step 9-()specimen4elastic modulus (MPa) step 80-(0)acouste emsio step 80-(0)specimen 5(a) modulus(b) AEV. CONCLUSIONA large-scale three-dimensional simulation was conducted using parallel computer approaches. Thefractural process of a beam model with soft layers under three point loading was simlated. In the conrse中国煤化工YHCNM HGVol.20, No. 2 Zhang Yafang et al: Fractural Process and Toughening Mechanism of Composites147.elastic modulus (MPa) step 86(0)acoustic emissin step 86 (0)specimen 6elastic modulus (MPa) step 80-(0)acoustic enisiono step 80-0)|xspecimen 7__28elastie modulus (MPa) step 90-()acoustie emission step 90-(0)specimen 8(间) modulus(b) AEFig. 6. Curves of fracture energy and peak load of the laminated models versus the strength of soft layer .of crack propagation, the crack will change direction when a soft layer is met. After propagating in thesoft layer a certain distance, the crack will turn back to the load direction again, where the distance isdetermined by the strength of the layer. With such a cyclic procedure, the fracture path is much longerthan that in a ceramic block. The energy dissipation mechanism, therefore, gives laminated ceramic atoughness better than that of the brittle ceramic material.Furthermore, the effect of the strength of soft layers has been investigated in details. Extremely highand low strength of the soft layers is not good at improving the toughness of the laminated compositeceramic. So, the strength of the soft layer should be designed property.Finally, as the fractural process and the location of cracks is difficult to be observed in laboratorytests, this simulation is helpful for further optimization to improve the characteristics of compositematerials.References] Clegg W.J, Kendall K,, Alford N.M., A simple way to make tough ceramics. Nature, 1990, 347(10): 445-447.2] de Portu G., Micele L, Pezzotti G., Lamninated ceramic structures from oxide systems. Composites: PartB, 2006, 37: 556-567.[3] Pinho S.T, Robinson P., Iannucci L, Fracture toughness of the tensile and compressive fibers failure modesin laminated composite. 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