Investigation On The Trans-scale Mechanical Behaviors Of The Interface Of Adhesively Bonded Systems

Compared with traditional mechanical joining techniques such as riveting and welding,adhesive bonding has many advantages,including lower structural weight,lower fabrication cost and more uniform stress distribution.Therefore,the adhesive bonding technology has been widely used in aerospace,automotive,electronics and construction industries.The interface is usually the weakest point of the adhesively bonded systems,and thus its deformation and failure behaviors directly affect the overall performance of the systems.Numerous experimental results have revealed that the interfacial stiffness,strength and critical energy release rate show obvious size effects when the adhesive layer thickness decreases from macro to micro scale.These size effects cannot be captured by the classical continuum mechanics since it is inherently scale-free.However,this can be done by the high-order continuum mechanics such as the strain gradient theory,considering that it incorporates the intrinsic length scales reflecting the material microstructure.In this work,on the basis of the strain gradient elasticity and the corresponding fracture criterion,we systematically investigate the deformation and fracture behaviors of the interface of macro/micro-scale adhesively bonded systems.The results can help us design strong and tough interface via adhesive bonding.The main contents and conclusions are summarized as follows:(1)In civil engineering,the fiber reinforced polymer plates are usually adhesively bonded to the concrete structures to realize structure reinforcement.In the previous study,an approximate analytical solution of the interfacial stresses in these thin plate/host beam structures is obtained by simplifying the deformation of the adhesive layer and assuming that two adherends have the same curvature.In this work,a rigorous analytical solution of the interfacial stresses and overall stiffness is obtained by abandoning the assumption of the same curvature of two adherends.When the thicknesses of two adherends are comparable,the rigorous analytical solution siginificantly improves the previous approximate analytical solution.And the rigorous analytical solution reveals the influences of the properties of the plate and interface on the interfacial stresses and overall stiffness.(2)Adhesively bonded stiff film/compliant substrate systems are common in flexible electronics,and the interfacial debonding is one of their main failure modes.In order to characterize the debonding process of stiff film/compliant substrate systems,we propose a two-dimensional theoretical model based on the bilinear cohesive zone model.Considering the substrate as an elastic half-plane leads to the interfacial shear stress appearing as a singular integral in the governing equations.By expanding into the first-kind Chebyshev polynomials and further adopting the collocation method,the interfacial shear stress can be solved.The solutions of the present model are verified by the previous experimental data and the finite element analysis.The results indicate that the present model can not only describe the full debonding process,which includes the elastic deformation and softening of the interface,but also capture the non-uniform deformation of the substrate.When the film modulus increases,the remote strain corresponding to the debonding initiation first decreases and then stabilizes at a certain value.(3)Micro-scale adhesive layers have been widely used in flexible electronics and microelectromechanical systems.By characterizing the adhesive layer with strain gradient elasticity,we propose a trans-scale mechanics model to predict the deformation of the macro/micro-scale adhesively bonded systems.The results indicate that when the adhesive layer thickness is comparable to the intrinsic length scale of the adhesive(usually on the order of microns),the interfacial tractions increase substantially and the adherend displacement decreases significantly.Meanwhile,the adherend displacement is insensitive to the adhesive modulus.These results reveal that the strain gradients in the constrained micro-scale adhesive layers can significantly increase the interfacial stiffness of adhesively bonded systems.(4)Numerous experimental results have revealed that the interfacial strength of adhesively bonded systems increases when the adhesive layer thickness decreases from several millimeters to hundreds of microns.On the basis of the strain gradient elasticity and the nominal-strain fracture criterion,a trans-scale mechanics model is proposed to characterize the thickness-dependent interfacial strength of the cylindrical scarf joints.The interfacial strengths predicted by this model match well with the previous experimental results.For a given adhesive layer thickness but varying scarf angles,the relation between the interfacial tension and shear strengths can be depicted by a circle,while the relation between the critical nominal tension and shear strains is described by an ellipse.As the adhesive gets thinner,the strength circle and the critical strain ellipse expand outward,indicating larger interfacial strength and critical strain due to the stronger strain gradient effect.The present study reveals the crucial role of the strain gradients in elevating the interfacial strength of micro-scale adhesively bonded systems.