DELAMINATION DURING BUCKLING OF COMPOSITE CONSTRUCTIONAL ELEMENTS

. Laminated constructional elements have widespread applications in aerospace. This paper presents of the buckling for E-Glass. Design solution based by the criteria of strength materials. The delamination of composite constructional elements is determined by the normal and shear stress. The non-linear strength criterion suggested by the author in case of complex state of stress.


Introduction
The delamination of composites depends on their matrix and the changed mechanical characteristics of reinforced elements during deformation. In the case of mechanical behaviour of laminated composites during compression the bending moment appears besides axial forces. The fibre experiences normal and shear stresses (Kim et al. 1998;Keller et al. 2004; Barbero et al. 1993; Barbero et al. 1999). Similar work was done while analysing the interfaces of I-beam shelves and walls (Bank et al. 1999), columns (Mosallam et al. 1992), beams (Bank et al. 1994), and cases of bar buckling depending on their geometry (Shu et al. 1993a;Shu et al. 1993b;Brewer et al. 1988). J. Brewer and P. Langace, as well as M. Fenske and A. Vizzini, suggested evaluation criteria for delamination. S. S. Wang and C. Hwu et al. tried solving the problems of composite fracture (Wang 1983;Hwu et al. 1995) The investigation of composite delamination remains topical, however, because the investigation and evaluation of fibre remain difficult.

Buckling of composite constructional elements
According to Euler's formula, critical buckling force is written as follows: where cr F -critical buckling force; E -modulus of elasticity; L -length of column; ef I -minimal moment of inertia.
The important characteristic of material is composite's modulus of elasticity C E . It can be calculated in the following way (Bai et al. 2009): where t -thickness of layer and indexes , v m and f mean cover, fiber and filling respectively.
The modulus of elasticity, v E , is accepted as resin. The composite's c E is received experimentally. Limit shear stresses lim τ are calculated in the following way (Bai et al. 2009) where U σ -ultimate strength and θ -angle of layers with regard to stretching axis. Lateral displacement is calculated as follows (Timoshenko et al. 1993) where w -lateral displacement; x -coordinate in the longitudinal direction of the plate; max w -maximal lateral displacement in the middle part of the plate during delamination.
Thus when the plate is compressed by force F , transverse forces Q will be received in the following way (Timoshenko et al. 1993

Strength criteria
In order to evaluate the strength of composites, various criteria are applied. One of the simplest is the Tresca criterion, which evaluates normal stresses and shear stresses (Fenske et al. 2001 where x σ -normal stresses and xy τ -shear stresses.
It has to be noted that normal stresses, y σ , in the direction of y axis and shear stresses, yz τ , on the yz plane are quite small and need not be taken into account. Then: where A -area of cross-section; M -bending moment. The normal stresses are calculated in the following way: where r V and f V are volumes of resin and reinforced elements, and n is the ratio of elasticity module of reinforcement and matrix. According to the yield criterion of von Mises (Bai et al. 2009 where Y σ -yield stress or The main stresses are calculated in the following way: We shall apply polynomial strength criteria (Vasiliev et al. 2007): where R and S -constants We find the constants R and S from the marginal conditions: Then equation (13) is as follows: The stresses 1 2 , σ σ are received: When the strength criterion is put in this form (Vasiliev et al. 2007 Then we write: According to experimental tests (Vasiliev et al. 2007), strength criterion (19) corresponds to experimental results better than criterion (15) and even more precisely than criteria (7) and (11).
Polynomial strength criteria show formal approximation of experimental data in the coordinates of principal axes, however. These criteria become more complex in other coordinates. Tensoric strength criteria are therefore applied. For example, when the orthotropic material moves from principal axes 1 and 2 to turned axes 1´ and 2΄ at the angle 0 45 φ = , the strength criterion is put in the following way: This criterion differs from the criterion (19) because new constant 12 R cannot be received, according to the conditions of equation (18).
Thus, the author suggests a tensoric criterion (Žiliukas 2006) , which is put in the following way: Then criterion (22) is put in the following way: When criterion (26) is written in non-linear form: we receive:

Delamination analysis
In order to solve the delamination problem of composite, we should apply strength criterion (25). Taking into account equation (3) Taking into account formula (9), and after we enter buckling force from formula (1) This formula determines the relation between the values of length cr L and shear angle cr θ when a straight bar or plate made from composite is being buckled.

Experimental tests
In order to do experimental tests, a 12-mm-thick composite plate was chosen. It is laminated by 0.5 mm v t = cover, the thickness of the resin is 2 mm In such a way, if we have various values of critical delamination angle cr θ , we can calculate the critical length of the plate. The calculation results are presented in table. According to table, the maximal critical length of the plates is received when the delamination angle is 0 30 .

Conclusions
1. The delamination of composite constructional elements is determined by the normal and shear stresses in the fiber. 2. The strength criteria used to evaluate the strength of composites are too complex because of the large number of constants and the difficulty of determining them. 3. The non-linear strength criterion suggested by the author for a complex state of stresses allows a simple dependency between critical delamination angles and critical lengths of the plate at buckling to be determined. 4. According to experimental and calculation data, the maximal critical length of the plate at buckling is received when the delamination angle is 0 30 .