Abstract

Perturbation(s) in the adhesive’s properties originating from the manufacturing, glue-line application method and in-service conditions, may lead to poor performance of bonded systems. Herein, the effect of such uncertainties on the adhesive stresses is analyzed via a probabilistic mechanics framework built on a continuum-based theoretical model. Firstly, a generic 2D plane stress/strain linear-elastic model for a composite double-lap joint with a functionally graded adhesive is proposed. The developed model is validated against the results obtained from an analogous finite element model for the cases of bonded joints with metal/composite adherends subjected to mechanical and thermal loadings. Subsequently, the proposed analytical model is reformulated in probabilistic mechanics framework where the elastic modulus of the adhesive is treated as a spatially varying stochastic field for the cases of homogeneous and graded adhesives. The former case represents stochastic nature of conventional joints with a homogeneous bondline while the later case showcases the perturbation in the properties of functionally graded joints. To propagate the uncertainty in the elastic modulus to shear and peel stresses, we use a non-intrusive polynomial chaos approach. For a standard deviation in the elastic modulus, the proposed model is utilized to evaluate the spatial distribution of shear and peel stresses in the adhesive, together with probability and cumulative distribution functions of their peaks. A systematic parametric study is further carried out to evaluate the effect of varying mean value of the adhesive’s Young’s moduli, overlap lengths and adhesive thicknesses on the coefficient of variation/standard deviation in peak stresses due to the presence of a random moduli field. It was observed that the joints with stiffer adhesives and longer bondlengths show smaller coefficient of variation in peak stresses. The findings from this study underscore that the predictive capability of the proposed model would be useful for the stochastic design of adhesively bonded joints.

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