On the non-axisymmetric behavior of quasi-isotropic woven fiber-reinforced composite Belleville springs

Abstract

Discussed is the development of an analysis for studying the deformation behavior of Belleville springs fabricated of fiber-reinforced composite materials. The springs are subjected to a compressive loading, and owing to the shallow conical geometry of a Belleville spring, snap-though behavior can be exhibited and thus geometric nonlinearities are taken into account. By considering cost and ease of fabrication, off-the-shelf textile materials along with standard resin transfer molding techniques are strong candidates for the production of composite Belleville springs. However, as textile materials typically employ fibers at fixed angles relative to some reference direction, e.g. (0°/90°), (0°/±45°), or (0°/±60°), using such textiles in a conical geometry results in overall material properties that vary in the circumferential direction. This could complicate the response, potentially preventing an axisymmetric behavior even though the loading is symmetric circumferentially. This article addresses these issues by presenting a mathematical model of a textile composite Belleville spring with spatially varying material properties, in addition to geometric nonlinearities. The minimum total potential energy principle and the Rayleigh–Ritz approach are used to approximate the mechanical behavior. Discussed are the material property variations, load-deformation behavior, and strains and stresses as a function of circumferential location. For the particular case considered, a four-layer [(0°/90°)/(+45°/−45°)]S glass-epoxy textile laminate, the kinematic response is, for all intents and purposes, axisymmetric, while the strain and stress responses are not.