MATERIALE PLASTICE ♦ 48♦ No. 2 ♦ 2011 http://www.revmaterialeplastice.ro 195 Study of Some Elastic Properties for Sandwich Beams Reinforced with Different Types of Fabric DUMITRU BOLCU 1 *, MARIUS MARINEL STANESCU 2 , ION CIUCA 3 , SONIA DEGERATU 4 , MARIUS-ALEXANDRU GROZEA 5 1 University of Craiova, Department of Mechanics, 165 Calea Bucureºti, 200620, Craiova, Romania 2 University of Craiova, Department of Applied Mathematics,13 A.I. Cuza, 200396, Craiova, Romania 3 Politehnica University of Bucharest,Department of Materials Science and Engineering, 313 Splaiul Independentei, 060042, Bucharest, Romania 4 University of Craiova,, Faculty for Engineering in Electromechanics, Environment and Industrial IT, Craiova, Romania. 5 Politehnica University of Bucharest, Strength of Materials Department, 313 Splaiul Independentei, 060042, Bucharest, Romania In this paper, we determined a state of stress, which verifies the Cauchy equations of equilibrium, the conditions of continuity on the surfaces between layers and boundary conditions for a sandwich beam subjected to tensile test. We customized the relations, previously obtained, for a composite beam consisting of two layers. Using a mediation formula for strain and stress, we obtained a new formula for the calculus of the longitudinal modulus of elasticity, when the constituent materials have different Poisson ratios. Considering the maximum stress reached in the layers, we determined a formula, which helps us to determine the order in which the two layers will break. We did experimental measurements for test samples made from polyesteric resin, reinforced with fiber glass fabric, carbon and carbon-kevlar. Keywords: composite materials, characteristic curve, elasticity modulus The composite plates and beams may be analyzed using many theories that differ mostly by including or neglecting the effects of angular strain and, rotational inertia, respectively. Hashin and Rosen use the classical theory [1], based on the hypothesis that a straight-line, normal on the median surface before deformation, remains straight and normal on the median surface during the deformation too. For laminates with a ratio between the modulus of elasticity E and the shear modulus G reaching values of 40 25 - , it be can proven that this theory overestimates the natural frequencies of the structure. Another theory (First – order Shear Deformation Theory – FSDT) was developed [2] and later modified [3]. This theory relies on a linear distribution of the shear stress and requests a correction factor similar with the one from isotropic plates. This theory states that a straight line normal to median plane before deformation remains straight without keeping the normality on the median surface during deformation. Exact theories rely on a non-linear distribution of shear stress along the thickness of the plate or beam. The inclusion of high order terms implies the inclusion of supplementary unknowns. Moreover, when fulfilling both the parabolic distribution of shear stress in thickness and the limit conditions on external surfaces, a correction factor is not necessary anymore. Based on this fact, it was developed a theory [4] (High – order Shear Deformation Theory – HSDT) where it is assumed that the stress and strains normal to the median plane are null. Another theory in which the stresses normal to the median plane are considered too, has been developed in [5-6] and removes a series of contradictions appearing in previous theories by accepting non linear factors of shear stress in thickness; they didn’t also neglect some of the normal stress obtained by the loading of the composite structure. In [7] were obtained theoretical results and experimental determinations. Using a matrix method were determined * email: dbolcu@yahoo.com the main elastic characteristics of composite materials and their variation depending on the volumetric proportion of reinforcement. The studies of the composite materials dynamics reserved a special place for sandwich beams made from several overlapped layers with similar thickness. Most studies refer to three layer sandwich beams, the middle layer having visco-elastic behavior and the inferior and superior layers having extra elastic and resilience properties. Other authors having similar studies on the behavior of these materials suggested the following: -there is a continuity of displacements and stress between layers; -there is no deformation along the thickness of the beam; -the transversal inertial forces are dominant, neglecting longitudinal inertia and rotational inertia of the beam section; -the external layers have elastic behaviour and are subject to pure bending and the core has elastic or visco- elastic behaviour taking over shear stress; - the core is not subject to normal stress. Based on these hypotheses, there have been developed models considered to be the fundamentals of DTMM theory [8-10]. Considering this theory, it was adapted a variation approach, obtained equations for sandwich plates taking also into consideration different angular deformation for the layers and managing to estimate the stress between the layers [11]. The most common types of damage in fibrous composites are fiber breakage, fiber/matrix debonding, matrix cracks, fiber kinking and for large diameter fibers, radial cracks in the fibers. We consider damage that can only increase or remain constant over time; there is no healing. As damage occurs, the material loses stiffness and exhibits nonlinear, inelastic response with permanent strains after unloading. The inelastic response is the result