Numerical modelling of multi-material graded joints under shear loading

Abstract

Due to environmental concerns, modern transportation solutions demand drastic reductions of fuel consumption and emissions, which can only be achieved with advanced structures using high-performance lightweight materials. For joining these dissimilar materials, adhesive bonding appears as an optimal solution, since mechanical fastening adds weight to the structure, and welding technology is not easily applicable to reinforced plastics and composites. However, one of the major drawbacks associated with bonded joints is the presence of stress concentrations at the overlap ends, especially in single lap joints. In order to reduce these stress concentrations, several techniques have been developed. One of these is the functionally graded adhesive, in which the adhesive properties gradually vary along the overlap length, leading to a more uniform stresses distribution and improving the joint strength. However, the manufacture of an adhesive layer with properties which gradually vary is complex in practice and so is the creation of numerical models that represent these configurations. In the present work, a numerical model for different-graded distribution of adhesive properties along the overlap was developed, using programmed step functions on finite element analysis background in order to discretize and simplify the continuous properties distribution gradient. Cohesive zone modelling was introduced in the numerical model, enabling it to effectively predict graded joint strength. The model was validated with experimental results of functionally graded joints available in the literature. The numerical model developed presents itself as a powerful tool to predict joint strength for functionally graded joints, without imposing large computational demands.

Numerical modelling of functionally graded adherends

“…The theoretical graded material evaluated on the present work has properties that range between a high strength steel (HSS) with Young's modulus of 210 GPa and density of 7.6 g/cm 3 and a fibre reinforced polymer (FRP) with Young's modulus of 30 GPa and density of 1.12 g/cm 3 .…”

“…3,19,36 For the adherends, quadratic 4-node plain strain quadrilateral elements referenced on the software library as CPE4R for the were used, while for the adhesive quadradic 4-node cohesive elements for the adhesive layer, referenced as COH2D4. 3,19,36 The adherends were divided in 21 layers with different stiffness properties, according to the distributional exponential laws evaluated as presented in Figure 4. It should be highlighted that the model evaluated on the present work considers that the adherends suffer no plastic deformation, being the damage only located on the adhesive layer.…”

“…Concerning of the numerical analysis, the CZM is stablished as a very accurate method, widely used to assess the strength of bonded joints, 3,15,19,36,37 and have been used in several works, once it was able to predict the failure load in several scenarios as impact, fatigue, mixed-adhesive and graded adhesive joints. 3,15,19,36,37 The use of CZM emulates the failure process on the bond line, through the application of elements with fracture toughness, strength and elasticity properties, which allow the model to simulate the crack nucleation, growing and propagation on the adhesive, when the failure criteria is reached in an element. 3,38 The ratio between the stress and displacement previously, during and after the crack initiation is ruled by a traction separation law.…”

“…3,15,19,36,37 The use of CZM emulates the failure process on the bond line, through the application of elements with fracture toughness, strength and elasticity properties, which allow the model to simulate the crack nucleation, growing and propagation on the adhesive, when the failure criteria is reached in an element. 3,38 The ratio between the stress and displacement previously, during and after the crack initiation is ruled by a traction separation law. 3,38 A triangular traction separation law was used to model the adhesive response, as presented in Figure 6.…”

“…The application of bonded joints has been growing in several industries, including the transportation, electrical, building, marine, oil and sports sectors. [1][2][3] These joints provide several benefits, among which are increased design flexibility, the capability of joining dissimilar materials, less stress concentration and lower structural weight in comparison with other joining techniques. 1,4 The geometry most used in practical applications is the single lap joint (SLJ), for being simple and efficient.…”