Method of Composite Materials Characteristics ... - Science Direct

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ScienceDirect Procedia Engineering 150 (2016) 1831 – 1836

International Conference on Industrial Engineering, ICIE 2016

Method of Composite Materials Characteristics Forecasting G.B. Verzhbovskiy* Rostov State University of Civil Engeneering, 162, Socialisticheskaya Street, Rostov-on-Don 344022, Russia

Abstract An analytical method for predicting characteristics of building composite materials is proposed. It is based on the properties of their components and on the following key assumptions: characteristics of a composite on the contact surfaces of the matrix and the filler are not worse than the parameters of any of the components of the material; the properties of the matrix are taken as isotropic and equal over the whole volume of the environment that is provided by the technology of preparation of mixtures; the filler of the composite consists of particles-grains which size is so small that their properties can be considered isotropic, however, the particles are still not nanoscale; the material as a whole and its components obey the Hooke's law and the rule of mixtures until the destruction of any part of the composite; the elastic stage of the work material is reviewed. The approach is more close to the experimental values of the ultimate strength and elastic modulus of the material than other techniques. © 2016 2016The TheAuthors. Authors. Published by Elsevier © Published by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the organizing committee of ICIE 2016. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICIE 2016 Keywords: ɫomposite materials; matrix; filler; forecasting characteristics; modulus of elasticity; Poisson's ratio

1. Introduction Almost all known modern construction materials are not found in nature because created by man and are artificial or composite. Composite – a heterogeneous solid material consisting of two or more components with a clear boundary between them. The first mention of it appears in the Old Testament (Exodus, CH. 5) [1]. Slaves of Ancient Egypt added straw to clay in the manufacture of bricks to reduce cracking during the drying products in the sun. Thus, the age of composite materials is calculated even not centuries, but millennia. In most composites components can be divided into matrix – binder and included reinforcing elements or fillers. In the materials of structural purpose of reinforcing elements usually provide the necessary mechanical properties –

* Corresponding author. Tel.: +7-906-415-4660. E-mail address: [email protected]

1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICIE 2016

doi:10.1016/j.proeng.2016.07.178

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G.B. Verzhbovskiy / Procedia Engineering 150 (2016) 1831 – 1836

strength, stiffness, etc., and the matrix is responsible for the joint operation of the reinforcing elements and protects them from mechanical damage and aggressive chemical environment [2, 3]. The mixture of matrix and filler is sometimes called composition, physical and mechanical characteristics which can vary within wide limits. 2. The relevance The mechanical behavior of the composition is defined by the properties of the reinforcing elements and matrix, as well as strength of connections between them. Characteristics of the created product and its properties depend on the choice of initial components and technology of their combination [4]. The result is a composition with a set of parameters, reflecting not only the original characteristics of its components, but also new properties, which isolated components do not possess. For example, the presence of interfaces between the reinforcing elements and the matrix significantly increases the toughness of the material [5, 6]. Due to the fact that the composition and percentage parts of composite materials can vary greatly, it is interesting to question the analytic determination of physical and mechanical characteristics of the composition at the stage of theoretical prediction. There is an enormous number of works which propose different approaches to its solution. All of them are to some extent approximate, as there is even a distinction of characteristics of composite material and its products [7]. Thus, the last word remains for experimental studies, however, at the stage of creation of the material analytical methods can be very useful. For considered in the present work, composite powder materials with a matrix structure of the main evaluation methods are the Voigt approaches, according to which all component parts of the composition have the same strain [8], and Reuss, who thought that same tension [9]. Known ways of narrowing the resulting plugs of values, for example, Hasina-Shtrikman or the Voigt-Reuss. In some works ([10], [11], etc.) provides methods for determining the physical properties of composite materials characteristics of components. The diversity of approaches to predictive analytical characterization of the composites can be traced in the works [12-16] and others. Polymeric particulate composites behave as a material that obeys Hooke's law and the rule of mixture [7]. In this connection it is of interest to develop analytical methods for the determination of approximate values of the basic physics-mechanical characteristics of the composites at various percentage ratios of their components. It is also advisable to restrict the range of fillers used and their mass fractions in the material under the condition of providing the minimum required values of elastic modulus and strength limits. 3. Statement of the problem Physic-mechanical properties of composites are determined by their structure and depend on the parameters of the matrix, filler and additives. Prediction of properties of artificial materials is an important issue. Despite the fact that numerous well-known works on mechanics of composites, to date, no single approach to the solution of this task, and obtained by different researchers value essential characteristics are or interval estimates, or give acceptable results only for certain compositions. Following [17, 18, 11, etc.] consider the output of one of the possible methods of predicting physical and mechanical characteristics of composites with the structure of the statistical mechanical mixture of isotropic components. Recall that the statistical mechanical mixtures called matrix environment in a representative volume which is provided by the uniformity of composition at complete randomness of orientation of the grains of the filler. To solve this problem, we introduce the following basic assumptions: x Composite characteristics on the contact surfaces of the matrix and filler is not worse than the parameters of any of the components of the material; x Properties of the matrix are taken isotropic and equal over the whole volume of the environment that is provided by the technology of preparation of mixtures; x Filler composite consists of particles-grains whose size is so small that their properties can be considered isotropic, however, the particles still are not Nano sized; x Material in general, and it components obey the Hooke's law and a mixture rule until the destruction of any part of the composite; x The elastic stage of the work material.

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4. The theoretical part The most important for load-bearing structures are their high strength properties, modulus of elasticity and shear, and Poisson's ratio, to determine which will use the hypothesis on the existence of the elastic potential [19]. According to it, the energy of mechanical deformation does not depend on the direction in question V j H j const , i.e. for any j. In [18] this hypothesis is used to mineral composite materials with similar properties of the matrix and filler and is approximately equal to the percentage amounts of these parts. It also States that the obtained formulas give large errors when significant differences in properties and/or volumes of the parts of the composite environment. It is known that the strain energy of a body is the sum of the energies of deformation of its individual parts [20]. Spread it on a two-component composite material, assuming that the elastic potentials between components there is a relationship defined by the expression:

sV 1H1

(1)

V 2H 2 ,

moreover, s is a coefficient, the value of which will be defined below, and the rest of the notation commonly used. In addition, the index "1" refers to matrix and "2" to the filler. Under triaxle compression, the relationship between stresses and relative deformations is expressed through the bulk modulus K:

V . H

K

(2)

According to the adopted assumptions, Hooke's law is performed for each component, so we can record

s

V 12 K1

V 22

V or 1 V2 K2

1

§ K1 · 2 1 2 ¨ ¸ s . © K2 ¹

(3)

Then from (1) and the generalized Hooke's law 1

V1

§ K1 · 2 ¨ ¸ V 2 , © sK 2 ¹

H1

§ K1 · 2 ¨ ¸ H2. © sK 2 ¹

(4)

1

(5)

Following [21], imagine the stress and strain in the composite via the volume average similar components of the matrix and filler:

V¦

V 1 m1 V 2 m2 ,

(6)

H¦

H1 m1 H 2 m2 .

(7)

In the last expressions, the index "Ȉ" refers to the composite as a whole, and m1 and m2 are volume fractions of matrix and filler, respectively, and m1 + m2 = 1. The expression (6) with (2) can be rewritten as follows:

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H ¦ K¦

(8)

H1 K1 m1 H 2 K 2 m2

Then, by considering together (7) and (8), we obtain

H1 H2

K ¦ K 2 m2 . K ¦ K1 m1

(9)

Similarly, formulas are written to evaluate stresses in components of the composite:

V1 V2

K1 K ¦ K 2 m2 K 2 K ¦ K1 m1

(10)

.

Equating (3) and (10) and performing transformations, we get the expression for determining the bulk modulus of two-component composite material K¦

K1 K 2

1

2

1

1

1

1

1

1

m1 K1 2 m2 K 2 2 s m1 K 2 2 m2 K1 2 s

2

.

(11)

2

The parameter s invited to take in the relationship view s

E1

E2

.

(12)

To find the other elastic constants is necessary to obtain analogous to (11) the expression of the shear modulus, and then, given the isotropy of the properties, find the modulus of elasticity and Poisson's ratio of the composite material. In the future, the reasoning continues to be provided for the absence of inelastic deformations in composites components and the ideal contact conditions on grain boundaries and matrix. In addition, it was assumed that the hypothesis of the existence of the elastic potential (1) is true for any stress state for uniaxial compression. Omitting intermediate calculations, we get the expression for finding shear modulus of the composite, coinciding by the form with (11): G¦

G1G2

1

2

1

1

1

1

1

1

m1G1 2 m2 G2 2 s m1G2 2 m2 G1 2 s

2

.

(13)

2

Expressions for modulus of elasticity and Poisson's ratio of two-component composite can be obtained taking into account known dependencies between elastic constants: E¦

9 K ¦ G¦ 3K ¦ G¦

, Q¦

3K ¦ 2G¦ 2 3K ¦ G¦

.

(14)

Note that the equality (14) is valid not only for the entire composite as a whole and for its parts, if we replace the subscripts.

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5. Practical results

As evidence of the applicability of this approach in table 1 shows the values of various characteristics of composite materials, experimentally defined, and the modules of the volumetric strain, calculated according to (15) with (16) and s=1, according to [18]. The table shows that the error in determining the modules in (15) for most compounds is not greater than 9% and only a very small percentage filler content is increased to 18%. In the last two columns of the table lists results for the case s=1, which show a larger discrepancy with the experimental data. Good agreement between experimental and theoretical values of modules of the volumetric strain of composite materials, such as vegetable and mineral fillers confirms the correctness of the expression (15). The influence of various additives that improve various qualities of composites can be accounted for by using correction factors. Table 1. The value of the module of volumetric deformation of composite materials with polypropylene matrix. Filler

Kɇexp.

20%woodflour

Kɇ(15)

%

Kɇ(S=1)

%

2854

3201

12,1

3615

26,6

30%woodflour

3262

3386

3,8

4012

23,0

40%woodflour

3873

3613

6,7

4448

14,9

50%woodflour

4281

3898

8,9

4930

15,2

60%woodflour

4689

4267

9,0

5463

16,5

70%woodflour

5199

4762

8,4

6058

16,5

80%woodflour

5668

5460

3,7

6724

18,6

3354

15,6

3883

33,9

3562

8,7

4263

9,3

3295

17,7

3473

24,0

3386

5,8

3595

12,3

3587

8,7

3851

16,7

30%chalk

2900

40%chalk

3900

25%talc

2800

30%talc

3200

40%talc

3300

s

0,14

0,16

0,4

6. Conclusion

Proposed in the article the method of forecasting characteristics of composite materials, the reliability of which is confirmed by the coincidence of the results with known solutions of particular problems [22], can serve to predict the properties of two-component polymer composite at the stage of its development and makes it possible to significantly reduce the number of required physical experiments [23]. The methodology can be extended to composites in the form of multicomponent mixtures (with two or more fillings), but the latter are not recommended for use in building structures of buildings and structures because of its high cost. References [1] A. Ungerov, The didactic books, The books of the Old Testament, Publishing house of the Moscow Patriarchate, Moscow, 2012. [2] J. Sendecki, Mechanics of composite materials, vol. 2, Mir, Moscow, 1978. [3] B.M. Yazyev, Thermal stresses and relaxation phenomena in polymers, in: Proceedings of the XXIX B. tech. the conference of the Penza GUS. (1997) 110. [4] A.I. Reutov, Reliability of products made of composite materials taking into account the statistical variability of their characteristics, Bulletin of the Tomsk Polytechnic University. 2 (2010) 58௅62. [5] V.E. Vil'deman, Y.V. Sokolkin, A.A. Tashkinov, Mechanics of inelastic deformation and fracture of composite materials, Nauka, Moscow, 1997. [6] A. Ochsner, Mechanics and Properties of Composed Materials and Structures, Springer-Verlag, Berlin Heidelberg, 2012. [7] V.I. Kovalev, The System Dyurisol, Ideas for Your home. 124 (2009) 76௅82. [8] V. Voigt, Textbook of Crystal Physics, Teubner, Berlin, 1928.

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[9] I.A. Tarasyuk, S.A. Kravchuk, A Narrowing of the fork Voigt-Reuss theory of structurally inhomogeneous elastic isotropic on the average composition of bodies without the use of variation principles, Electronic scientific journal APRIORI, Series: Natural and technical Sciences. 3 (2014) 1௅18. [10] R.G. Petrochenkov, Composites of mineral fillers, vol. 2, Publishing house of Moscow state mining University, Moscow, 2005. [11] V.B. Rabkin, R.F. Kozlov, Thermal expansion molybdate-copper and tungsten-copper pseudoalloys, Powder metallurgy. 3 (1968) 64௅70. [12] J. Gurland, The destruction of the composites with particles in a metal matrix, Fracture and fatigue, Mir, Moscow, 1978. [13] S.V. Kurin, Prediction of modulus of polymer composite materials for engineering products, Ph.D. diss., Naberezhnye Chelny, 2011. [14] S. Abrate, Impact Engineering of Composite Structures, CISM Courses and Lectures. 526 (2011) 411. [15] A.K. Kaw, Mechanics of Composite Materials, Taylor & Francis Group, London-NewYork, 2006. [16] G.W. Milton, The Theory of Composites, University Press, Cambridge, 2004. [17] G.M. Bartenev, J.V. Zelenev, Physics and mechanics of polymers, Higher school, Moscow, 1983. [18] Yu.N. Kazakov, Promising pre-fabricated buildings, Modern problems of construction industry, in: Proc. of Dokl. scientific.-tech. Conf. VS, SPb. (1997) 25௅26. [19] A.R. Rzhanitsyn, Theory of calculation of building structures on the reliability, Moscow, 1978. [20] Y.V. Nemirovsky, B.S. Reznikov, Strength of structural elements made of composite materials, Nauka, Novosibirsk, 1986. [21] G.G. Carlsen, Construction of wood and plastics, SI, Moscow, 1986. [22] A.V. Berezin, A.I. Kasenkina, Features of diagnostics of damage and durability assessment of composites, Mechanics of composite materials and structures. 1 (1999) 99௅20. [23] G.B. Verzhbovskiy, Low-rise prefabricated buildings and structures made of composite materials, LLC Publishing Bar, Rostov n/D, 2015.