On determining the mechanical properties of nonlinear-elastic composite materials

Abstract

Experimental determination of mechanical properties of unidirectionally reinforced composite materials (UCM) involves well-known difficulties due to the fact that materials in the form of tapes and braids have small transverse dimensions. Moreover, the behavior of UCM as structural members differs from that in independent tests.In this paper, we consider an approach that allows one to obtain information on the mechanical properties of a composite from experimental tests of structures made of this composite material (CM) [1][2][3]. The plane stress state of CM entering into a multilayer structure is studied. Examples of such structures are thin shells formed by winding or application of CM. However, certain difficulties arise here. They are due to "the fact that, when the elastic moduli are greatly different, the desired small quantities (for example, u12, E2, and G) change significantly with small variations of initial experimental data [3]. Problems of processing experimental data for nonlinear elasticity are studied, the calculation results of test problems are analyzed, and conditions imposed on an experiment are formulated.1. We formulate the necessary relations obtained in [2]. We investigate objects such as thin multilayer plates and shells formed by application or winding of reinforced orthotropic layers. We relate the Cartesian coordinate system x 1, x 2 to a reinforced layer by directing the x I axis along the axis of orthotropy having maximum stiffness and the x 2 axis perpendicular to the x 1 axis in the plane of the layer (Fig. 1).The relationship between stresses g~ and strains ~ in an arbitrary coordinate system ~71, :~2 obtained from the system xlx 2 by rotation about the x 3 axis in the plane of the tape for small strains is expressed in tensor form as we study materials whose longitudinal, transverse, and shearing stiffnesses differ greatly. An asymptotic analysis of constitutive relations (1.1) for materials of this class was performed byKazan' State Architect-Building Academy, Kazan' 420043.

Identification of the mechanical characteristics of composite materials from experimental data of shells of revolution

“…The latter can be obtained for the case where we consider the problem of determ~n;ng the linear elastic stiffness characteristics of an orthotropic m~terial, based on the results of measurements at two points of the meri&~n at (P(n) = ~(1)-These restrictions follow from the expression for the determinant and have the same form, as presented in [4]: (1) (ii)…”

“…Moreover, these characteristics can be different for each product, which is associated, for example, with influence of the technological factors as well as operating conditions within a particular structure on the properties of materials. Some methods make it possible to determine the mechanical properties of composite materials by analyzing the data obtained from the tests on multilayered specimens (see, for example, [1][2][3][4]). Indirectly, they take into account the technological factors of producing the material, dependence of the properties of CM on the methods of forming the structure, as well as its operating conditions, and allow us to overcome these technical difficulties..…”

“…Some methods make it possible to determine the mechanical properties of composite materials by analyzing the data obtained from the tests on multilayered specimens (see, for example, [1][2][3][4]). Indirectly, they take into account the technological factors of producing the material, dependence of the properties of CM on the methods of forming the structure, as well as its operating conditions, and allow us to overcome these technical difficulties..In [3,4], methods were described for determining the mechanical characteristics of band-type CMs based on the analysis of experiments carried out on cylindrical shells. A necessary requirement was the availability of at least two cylindrical shells with different winding angles.…”