Effect of the geometric, structural and dimensional differences to fiber reinforced composites.

Chiru, Anghel ; Goia, Ioan ; Modrea, Arina 等

1. INTRODUCTION

In the manufacturing process of a fiber reinforced composite there are many causes that produce difference between the theoretical model and the real ones. These differences conduce to differences between the computed values of the elastic constants of the material and the real comportment of this. In the paper are analyzed these differenced in order to correct the formulas known for the engineering constants calculus.

2. GEOMETRIC, STRUCTURAL AND DIMENSIONAL DIFFERENCES

In the following are presented some of the current difference that there are between the theoretical model and the real composite material. This analysis is focus on the fiber reinforced composites.

The real modality to manufacturer the composite conduces to many points where the theoretical arrangement can not be respected. For these reasons can appear difference between the theoretical dimensions, structures or shape and the real characteristic obtained after the manufacturer process.

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In Fig. 2 and Fig. 3 are presented some of determined micrographs of a composite material. It is easy to observe the existing differences between the theoretical models and the real arrangements. These differences conduce to difference between the computed values of the engineering constants and the values obtained via experimentations. The aim of this section is to identify these differences for o composite with cylindrical, parallel and long fibers.

For the long fibers, cylindrical and parallel, it is considered that they are made by circular cylinders arrange into a regular network. The most common network considered is the hexagonal arrangement (for this case the resulting material is transversally isotropic) (Hashin, 1965); (Hill, 1965). The composite is considered obtained by the repetition of the basic cell (hexagonal in our case), (Goia & Modrea, 1999). The real modality to manufacturer the composite conduces to many points where the theoretical arrangement can not be respected. For these reasons can appear difference between the theoretical dimensions, structures or shape and the real characteristic obtained after the manufacturer process.

3. SOME CONSIDERATIONS

From the presented examples it can be observed that during the manufacturer process, but too after this, during the use of the composite, can appear many differences between the real and the theoretic model of the composite. The made analyze can identify the following differences between the real composite and the theoretical model:

* Differences between the size of the mechanical characteristic of the matrix and of the fiber and the real values;

* Differences between the geometric shape of the materials for reinforce and the real geometric shape. For example, is difficult to obtain circular cylindrical fibers and the real shape will be generally, elliptic, with variable semi-axes ratio.

* Dimensional differences between the fibers of the same composite. In this case is necessary to know the distribution of these properties to realize a better calculus.

* Difference in the geometrical arrangement of the fibers. In the mechanical models is considered that the fiber are disposed into a regular geometric network (hexagonal, quadratic, etc). In the reality the arrangement can be very different.

All these differences will have an influence on the computed values and it is necessary to do an analyse to determine which formulas obtained in prevoius papers is better to use. It is obvious that is necessary a great effort to analyse the existing relations and in the same time is necessary to make experience to compare the computed values with the values obtained by experience(Milton & Kohn, 1988).

4. INFLUENCE OF THE DIMENSIONAL DIFFERENCE ON THE VALUES OF THE MECHANICAL CONSTANTS

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In the following we will make a numerical analysis of the formulas propose in the literature to determine the sensitivity of these formulas to different variations of the parameters that describe the composite materials, presented in Fig. 4 and Fig. 5 (Modrea; 2001, a, b, c).

5. CONCLUSIONS

The analyse made for the relations presented to calculus of the engineering constants conduce to the conclusion that small variations of the properties of the fiber or of the matrix can produce variations, sometime very large, of the properties of the composite material. The properties associated to the longitudinal comportament of the fiber reinforced composite, that generally are described by formulas that respect, aproximativelly, the mixture law have a linear variation with the properties of the components. For example is the case of the bulk modulus and the Young's modulus. The Poisson ratio is not sensitive to different variations of the parameters describing the composite material. The values of the properties that describe the transversal comportment of the composite are very different in comparison with experimental determined values. This is determined by the fact that the models are less perfect to study the transversal properties and better for the longitudinal properties.

A general conclusion is that is necessary to consider the real dimension, shape and structure of a composite. The difference that exists between the theoretical model and the real composite can conduce to large variation of the computed values and the composite can have different properties.

6. REFERENCES

Goia, I., Modrea, A., s.a. (1999). Calculus of the Mechanical Properties for the Composite Materials. A IX-a Conferinta internationald CONAT, (IXth CONAT International Conference), Brasov

Hashin, Z. (1965). On the Elastic Behaviour of Fiber Reinforced Materials of Arbitrary Transverse Phase Geometry. J. Mech.Phys. Solids. Vol.13, pp. 119-134.

Hill, R. (1965). A Self-Consistent Mechanics of Composite Materials. J. Mech. Phys. Solids. Vol.13, pp. 213-232.

Milton, G.W., Kohn, R.V. (1988). Variational Bounds on the Effective Moduli of Anisotropic Composites. J. Mech. Phys. Solids, Vol. 36, No.6, pp. 597-629

Modrea, A. (1998). Evaluarea parametrilor mecanici omogenizati pentru un material alcatuit din mai multe componente. A XXII-A Conferinta Nationala De Mecanica Solidelor, (XXIIth National Conference of solids mechanics), Brasov

Modrea, A., s.a. (2001, a). Evaluation of the elastic parameter for a composite when the strain/stress field is obtained via finite element method. A III-a Conferinta de dinamica masinilor (IIIrd Dynamics cars Conference), pp. 365-370, Brasov

Modrea, A., s.a. (2001, b). Evalution of homogenized coefficients for fiber reinforced plastic. A III-a Conferinta de dinamica masinilor (IIIrd Dynamics cars Conference), pp. 371-374, Brasov

Modrea, A., s.a. (2001, c). Mathematical Background for Evaluation of Homogenized Coefficients for Fiber Reinforced Plastic (FRP). A III-a Conferinfd de dinamica masinilor (IIIrd Dynamics cars Conference), pp. 375-378, Brasov