2010 - numerical studyon properties ofweak interlayer of laminated composite

8/12/2019 2010 - Numerical Studyon Properties Ofweak Interlayer of Laminated Composite

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232 ACTA MECHANICA SOLIDA SINICA 2010

by Weibull function. Base on this assumption and principles of finite element method, the numericalmodel could be generated to simulate not only the stress field but also the whole cracking process andthe toughening mechanism of LC. Simultaneously, the effect of strength and elastic modulus of the weakinterlayer and its thickness on both strength and toughness of laminated composite has been studiedin details for the purpose of optimizing the properties of LC.

II. NUMERICAL MODELINGIn previous studies of this field, material in numerical simulation was almost treated as homogeneous

media which is not the actual situation, strictly speaking. Various microscopic defects and propertydifference of materials on meso-level will cause inhomogeneity in macro mechanical properties of thematerial. For the purpose of involving the inhomogeneity into numerical modeling, a commercial FEMsoftware RFPA2D (Realistic Failure Process Analysis 2D)[4]is used in this study. With RFPA2D, thesample is modeled as numbers of rectangular cells with four nodes, the properties of each cell will be setby using Weibull distribution function. So the macroscopic nonlinearity could be obtained by generatinginhomogeneous meso-level cells. The probability density function of the adopted two parameters Weibullfunction is as follows:

f() =m

0

0

m1 e

0

m

(1)

where stands for mechanical characteristic parameter, like elastic modulus, strength, Poissons ratioand etc. 0 is the mean value of. m is the shape factor of Weibull, defined as homogeneity index ofthe material. The larger the shape factorm is, the more homogeneous the material will be.f() is the

so called probability density function.With RFPA2D, the initiation, development, coalescence and final failure of the crack can be simulated.

It is assumed that in each meso-level cell, the elastic damage constitution law could be adopted; Hence,Eq.(2) could be obtained in accordance with principle of strain equivalence.

=

E =

E0=

(1 D)E0(2)

where E0 is the initialized elastic modulus, Eis the effective elastic modulus induced by damageD .Generally speaking, 0 D 1. WhenD = 0, no damage exists; whileD = 1, the sample is completelydamaged and no carrying loading.

Each meso-level cell is initialized as elastic and when the stress of the cell increases, damage couldhappen if a pre-set damage criterion (either stress or strain) is met. In this study, modified Coulombcriterion is adopted, which could be described as: (a) the maximum tensile stress principle, i.e. thedamage will occur when the stress exceeds the allowable tensile stress (Eq.(3)); and (b) Moor-Coulombcriterion, i.e. shear damage could happen when the stress field touches the Moor Coulomb circle (seeEq.(4)).

1 t (3)

and/or1 + sin

1 sin1 3 c (4)

where is the frictional angle. 1and 3are the maximum and minimum principal stresses, respectively.t andc are the uniaxial tensile and compressive strength, respectively.

During the present simulation, the displacement control is used, i.e. with an initialized zero displace-ment and a given increment. In each step, the stress field will be calculated under given displacementcondition and in each cell whether the failure criterion is met will be checked. Then the calculation will

move to next step until the final failure happens in the sample.A three-point bending beam model once adopted in Phillips & Cleggs work [5] will also be used in

this study. As shown in Fig.1, the beam with 90 mm500 mm has been divided into 90500 cells. Thebeam has 15 layers. Among them, 8 layers (10 mm thick each) are set to be hard matrix while other7 layers (1 mm thick each) are set to be weak. To simplify the calculation, no interface between thematrix layer and weak interlayer has been set, which is different to the previous study. The thicknessratioTr (defined as thickness of all matrix layers over thickness of all weak layers) could be calculated


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Vol. 23, No. 3 Yafang Zhang et al.: Properties of Weak Interlayer of Laminated Composite 235

Finally, from Fig.5, as also stated by Chartier[12], Harmer[13], and Tang[14], a conclusion can bedrawn that both strength and toughness of LC model have been improved. This is quite different toother traditional toughening method, with which strength is always a victim of toughness. This couldbe summarized as an advantage of LC with weak interlayer, provided that the properties of such weakinterlayer are carefully set.

3.2. Effect of Strength of Weak Interlayer on Properties of LC

In the second group tests, six samples with different strength have been used. Samples have the

same dimension andTr as the previous section, i.e. Tr = 9/1. The properties of the matrix are keptthe same too. However, the properties of the weak interlayer are reset as Table 2.

Table 2. Properties of the weak interlayer in Group 2 samples

Material Elastic modulus (GPa) Ultimate Strength (MPa) Poissons ratio

Sample 1 60(20) 30(20) 0.3(100)Sample 2 60(20) 50(20) 0.3(100)Sample 3 60(20) 70(20) 0.3(100)Sample 4 60(20) 100(20) 0.3(100)Sample 5 60(20) 125(20) 0.3(100)Sample 6 60(20) 150(20) 0.3(100)

Note, figures in parentheses are value of m, the index of homogeneity

Curves of relative fracture workWc/Wdand relative strengthSc/Sdof LC models versus the strengthof weak layer are presented in Figs.6(a) and 6(b), respectively.

Within the property range given in this study, a conclusion could be made that, there exists anoptimized strength of the weak interlayer which could get the best toughness and strength of LCsimultaneously. From Fig.6, when the weak interlayer is soft enough (Sample 1), both Wc/Wd andSc/Sd are low. Then both Wc/Wd andSc/Sd increase as the strength of the weak interlayer increasesuntil the curve passes its peak point (Sample 3).

This conclusion can also be supported by anatomizing the crack process of the six samples as shownin Figs.7(a) to 7(f). In Samples 1 and 2, the strength of the weak layer is relatively low, as a result, cracksinitiate and coalesce as usual; However, they cannot penetrate through the matrix layer and developmostly in the weak layers. Although Wc/Wd is in the range of 2 to 3.5, which means the toughnesshave been improved,Sc/Sd is still in the range of 0.9 to 1.1 which means the strength of LC is almost

the same as the matrix, or even a litter lower. For Sample 3 (see Fig.7(c)), both maximum values ofWc/WdandSc/Sdare achieved. The crack develops in the matrix and the weak interlayer alternatively;More energy is dissipated in such kind of crack deflection. Both matrix and weak interlayer play goodrole in supporting the LC to get an optimal toughness and strength, which means the properties ofthe weak interlayer suitably match the ones of the matrix. Furthermore, with higher strength of weaklayers (Samples 4 to 6), cracks cannot develop easily in weak layers, less deflection but more penetrationcracks appear. Both the amount and the length of horizontal cracks decrease when the strength of weak

Fig. 6. Wc/Wd andSc/Sd of LC models versus the strength of weak layer.


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Fig. 7. Failure Process of LC Model, Group 2 and 6 samples.

interlayer increases and less energy is needed. The toughness of LC drops down quickly and the failurepattern is getting similar to the one of the pure matrix, which implies that LC is getting to behave likebrittle material.

In addition, this conclusion can be verified by the laboratory tests carried out by Cai[8], Zan[9],Qian[15], and Tan[16].

3.3. Effect of Elastic Modulus of Weak Interlayer on Properties of LC

The third group test is carried out to study the effect of the elastic modulus of the weak interlayer.Samples have the same dimension andTr as previous sections. The properties of the matrix are keptunchanged too while the properties of the weak interlayer of eight samples of this group are summarizedin Table 3.

Curves of the relative fracture work Wc/Wd and the relative strength Sc/Sd of LC models versusthe elastic modulus of the weak interlayer are given in Figs.8(a) and 8(b), respectively. The optimized

Table 3. Properties of the weak interlayer

Elastic Modulus (GPa) Ultimate Strength (MPa) Poissons Ratio

Sample 1 10(20) 70(20) 0.3(100)

Sample 2 20(20) 70(20) 0.3(100)Sample 3 30(20) 70(20) 0.3(100)Sample 4 40(20) 70(20) 0.3(100)Sample 5 50(20) 70(20) 0.3(100)Sample 6 60(20) 70(20) 0.3(100)Sample 7 70(20) 70(20) 0.3(100)Sample 8 80(20) 70(20) 0.3(100)

Note, figures in parentheses are value ofm, the index of homogeneity

Fig. 8. Wc/Wd and Sc/Sd of each sample versus the elastic modulus of the weak layer.


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Fig. 10. Variations ofWc/Wd and Sc/Sd of LC models withTr.

has some extent of improvement as Wc/Wd reaches about 2.0. With Tr further increasing, the weakinterlayer becomes thin, but the relative fracture work and the higher the relative strength increase.For Sample 9, especially, whenTr is taken to 9/1, the fracture work increases dramatically.

Generally speaking, the thicker the weak interlayer, the worse the toughening effect. In the laboratorytest published by Guo et al.[17], Yang et al.[18], similar conclusions can be made.

Particularly, laboratory tests on Bi3N4/BN laminated ceramic composite with different thicknessratios produced by using tape-casting method were carried out by Guo et al.[19]. Their results on thefracture work and the strength are presented in Fig.11. Comparing to Fig.10, only the trend keepssimilar while there is big discrepancy in values. This only illustrates that the direction of this numerical

simulation could be right and practicable in further structural optimization. Moreover, the reason forthe discrepancy could be as followings: (a) The actual parameters of Bi3N4/BN laminated ceramiccomposite are not the same as used in the numerical simulation; (b) In experiment, for workmanshiprequirement of tape-casting to ensure the flowability and formability of ceramic slurry, some organicbinder and other additives should be added into the slurry, which may also bring some changes tothe properties of the matrix. These factors should be considered in the numerical simulation if moreaccuracy is expected in the future.

Fig. 11. Experimental fracture work and strength vs. Tr (extracted from Guo et al.[19]).

IV. CONCLUSIONSBy carrying out a series of numerical simulations on major properties of weak interlayer added in the

brittle matrix, the crack process and the toughening mechanism have been studied. In the tested value

range, many published laboratory tests can be verified through this numerical study. One particularpoint is that, with the weak interlayer added, the strength is no longer a victim of toughness. There is achance to improve both toughness and strength of the brittle material simultaneously, if the propertiesof the weak interlayer are well tuned.

The most suitable strength, the elastic modulus of the weak interlayer and the thickness ratio can beconcluded within the given range of property values. In this study, when the strength of the weak layeris about 30% of the matrix, the elastic modulus is close to the matrix or a little higher, and the thickness


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Vol. 23, No. 3 Yafang Zhang et al.: Properties of Weak Interlayer of Laminated Composite 239

is as thinner as possible (Tr= 9/1 in this study), subjected to the requirement of workmanship, bothtoughness and strength of the LC could be improved to their optimum.

Finally, this study shows that, the numerical simulation provides flexibility and also a powerfultool for designers to conduct optimization works in the field of LC toughening. One can try differentmaterials, different structures and different parameters of LC with assistance of the numerical techniqueadopted in this study.

References

[1] Li,D.Y., Qiao,G.J. and Jing,Z.H., Recent development in research of laminated ceramic composites.Journalof Inorganic Materials, 2002, 17(1): 10-16.[2] Cook,J., Gordon,J.E., Evans,C.C. and Marsh,D.M., A mechanism for the control of crack propagation in

all-brittle systems. In: Proceedings of the Royal Society of London, Mathematical and Physical Sciences,1964, 282: 508-520.

[3] Clegg,W.J., Kendall,K. and Alford,N.M., A simple way to make tough ceramics.Nature, 1990, 347(10):445-447.

[4] Tang,C.A., Wang,S.H. and Fu,Y.F., Numerical Test on Rock Failure Process. Beijing: Science and Tech-nology Publisher, 2003: 42-43.

[5] Phillips,A.J. and Clegg,W.J., Fracture behaviour of ceramic lamination in bending I. Modeling of crackpropagation. Acta Metall Materials, 1993, 41(3): 805-817.

[6] Guo,H., Huang,Y. and Li,J.B.. Properties and structure of Si3N4 laminated composite ceramics.Journalof the Chinese Ceramic Society, 1997, 25(5): 532-536.

[7] Clegg,W.J., The fabrication and failure of Laminar ceramic composites.Acta Materials, 1992, 40(11): 3085-

3093.[8] Cai,S.Y., Li,J.L., Xie,Z.P. and Huang,Y., Influence of interfacial b onding of Si3N4 laminated composites

on the mechanical properties. Acta Materiae Compositetae Sinica, 1999, 16(2): 110-115.[9] Zan,Q.F., Cai,S.Y. and Huang,Y., The influence of the toughness on the component of soft-layer in the

Si3N4/BN multilayered materials. ShanDong Ceramics, 1999, 22(2): 4-8.[10] Yi,X.S., New Development in Traditional Composite. Composite, Wu,R.J. ed. TianJin: TianJin University

Press, 2002: 136.[11] Zhang,Y.F., Tang,C.A., Zhang,Y.B. and Liang,Z.Z., Fracctural process and toughening mechanism 0f lam-

inated creamic composites. Acta Mechanica Solida Sinica, 2007, 20(2): 141-148.[12] Chartier,T., Merle,D. and Besson,J.L, Laminar ceramic composites. Journal of the European Ceramic So-

ciety, 1995, 15(2): 101-107[13] Harmer,M.P., Chan,H.M. and Miller,G.A., Unique opportunities for microstructureal engineering with du-

plex and laminar ceramic composites. Journal of the American Ceramic Society, 1992, 75(7): 1715-1728.[14] Tang,T., Zhang,D.M. and Fu,Z.Y., The research process of laminar ceramic composites. Ceramic, 2001,

154(6): 7-9.[15] Qian,X.Q., Ge,M.Z., Wu,Y.B. and Yang,H., Reinforcement mechanisms and optimum design of laminated

ceramic composites. Journal of Inorganic Materials, 1999, 14(4)520-526.[16] Tan,Y., Yang,H. and Ge,M.Z., Technique of preparation of laminated composite ceramic and the properties

of its interface. Journal of Ceramics, 1997, 18(2):113-117.[17] Guo,X.H., Cai,Q.H., Wang,C.A. and Huang,Y., A mechanics analysis of strengthening toughening design

of multilayer structure ceramics. Acta Mechanica Solida Sinica, 2000, 21(4): 313-324.[18] Yang,H. and Ge,M.Z., Metal Processing and Development in Research, Vol II. Beijing: Chemical Industry

Press, 1996.[19] Guo,X.H., Hu,N., Cai,Q.H., Zheng,Q.S., Zan,Q.F., Wang,C.A. and Huang,Y., A numerical simulation and

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2010 - numerical studyon properties ofweak interlayer of laminated composite

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