2019 Volume 75 Issue 2 Pages I_31-I_40
Spatially random variation of stress appearing in adhesive for a steel plate bonded by a CFRP plate is theoretically discussed by taking into account spatially random variation of longitudinal elastic modulus and shear elastic modulus associated with the adhesive. First, a new probabilistic model is proposed for describing spatially random variation of a longitudinal elastic modulus, shear elastic modulus and Poisson ratio of the adhesive, in which statistical correlation among these factors is introduced. Then, a system of differential equation of static mechanics describing axial force of the steel plate and shear force of the CFRP plate is extended to a system of spatially random differential equations. By constructing a numerically solving scheme for them, a probability distribution of a maximum of principal stress of the adhesive is estimated through computer simulations to generate solution of the system of random differential equations, which is directly applied to estimate probability of detachment of the adhesive. It is clarified that (i) probability distribution of a maximum of principal stress of the adhesive is well approximated by Gaussian distribution and (ii) probability of detachment of the adhesive is hardly affected by statistical correlation among longitudinal elastic modulus and shear elastic modulus of the adhesive.
