Construction of a one-layer equivalent model for a base material strengthened by two-layer bonded CFRP plates under bending load

Abstract

A simplified probabilistic model is newly developed to give equivalent description for a strengthening method using two-layer CFRP plates bonded to base components by adhesion. First, a system of simultaneous differential equations for the shear and vertical stresses acting on the adhesives are derived. In order to reflect the variation of debonding, it is extended to a system of random differential equations by considering the spatially random variations of the adhesive thickness. Then, in order to reduce the degree of freedom of the system for two-layer CFRP plates, a one-layer equivalent model is newly developed to give almost equivalent result on the probabilistic properties associated with debonding of adhesives in two-layer model, where equivalency is achieved from two points of view; one is a mechanical condition and the other is a fine adjustment on probabilistic factors. Finally, numerical examples are shown to validate the proposed equivalent model, in which Monte Carlo method is applied to estimate the probability of debonding. The results indicate that the proposed model can give appropriate estimation for the probability of debonding, only with reasonably reduced computing efforts.