Comprehensive numerical analysis of stress state in adhesive layer of joint including thermal residual stress and material non-linearity

Abstract: The main objective of this work is to improve understanding of the stress state in the adhesive layer of bonded joints and identify key parameters which govern performance of adhesive joints. This information is crucial for the prediction of the failure initiation and propagation with the further estimation of the durability and strength of adhesively bonded structures.A systematic numerical analysis of stress state in the adhesive layer of a single-lap and double- lap joint under various loading conditions (thermal and mechanical loading) and an alternative methodology to predict the direction for crack propagation within adhesive layer are presented in this thesis.  To identification of the most important parameters of joints is done based on the assessment of the peel and shear stress distributions in the adhesive layer. The thermal residual stresses arising after assembling of joints at elevated temperature are accounted for in the analysis.Initially, accurate, realistic 3D finite element model with novel boundary conditions (displacement coupling) was developed and validated. The employed boundary conditions allow to eliminate the edge effect and simulate the behavior of an infinite plate of composite laminate with off-axis layers (monoclinic materials). It is also possible to decouple the edge effects induced by the finite specimen width from the interaction with ends of the joint overlap region. Due to these advanced setting it is possible to eliminate influence of some of the parameters as well as to reduce geometry of the model without losing precision. Thus, the model is optimized with respect to the number of elements as well as element size distribution and does not require excessive computational power to obtain accurate stress distributions even near to the possible sites with stress perturbations (e.g. corners, cracks, etc). Additionally to the geometrical parameters, various material models have been employed in simulations of adhesive joints. A linear and non-linear material models (adherend and adhesive) was used for the single-lap joint, while a linear material behavior was considered for double-lap joint. The geometrical non-linearity was also included in the analysis whenever required. To make results more general and applicable to a wide range of different joints the normalized (with respect to the thickness of adhesive layer) dimensions of joints were used. Depending on the analyzed type of joint (single- or double- lap), combination of similar and dissimilar (hybrid) materials for adherends are considered: a) metal-metal; b) composite-composite; c) composite-metal. In case of the composite adherend (carbon and/or glass fibers) different laminate lay-ups were selected: uni-directional ([08]T and [908]T) and quasi-isotropic ([0/45/90/-45]S and [90/45/0/-45]S). In general, discussion and conclusions concerning the importance of various joint parameters are based on the magnitude of the peel and shear stress concentration at the ends of the overlap. In order to identify general trends with respect to the influence of mechanical properties of adherends the master curves for shear and peel stresses are constructed and analyzed. To simulate effect of the residual thermal stresses on the behavior of joints different methods for assembly of joints were considered (using dedicated adhesive or employing co-curing method). The results of this investigation lead to the conclusions that the one of the most important factors affecting the simulation results is the sequences of application of thermo-mechanical loading for different assembly methods. It is shown that simple superposition of thermal and mechanical stresses (most common approach) in the adhesive layer works properly only for linear material but it gives inaccurate results if non-linear material is considered. The thesis demonstrates the appropriate way to combine thermal and mechanical loads to obtain correct stress distributions for any material (linear and non-linear). The analysis of the influence of residual thermal stresses has shown that the peel and shear stress concentration at the ends of overlap joint and the shear stress within the over-lap region are reduced due to thermal effect. In case of composite adherend the co-curing assembly method is more favorable (in terms of reducing stress concentrations) than using adhesive for joining the materials.Finally, the simulation of the crack propagation within the adhesive layer for the bi-material (steel and composite) DCB sample with thick adhesive layer was carried out. The alternative to traditional fracture mechanics approach is proposed for the prediction of the crack path in the adhesive layer: a maximum hoop stress criterion. The hoop stress on the perimeters of a relatively large circle around the crack tip is evaluated to predict the direction of the crack extension with respect to the existing crack. The fracture mechanics is used to validate this approach and it is proved that if the Mode I is dominant for the crack propagation the hoop stress criterion be successfully used to predict crack path in the adhesive layer. This methodology is much more effective (in terms of required time and resources) than energy release based criterion or even X-FEM.The main result of this thesis is a tool to obtain accurate stress distributions in the adhesive layer of joints. This tool provided better understanding of the behavior of adhesive joints and allowed to develop new approach for prediction of crack propagation in the adhesive layer. This is definitely a development in the design of stronger, more durable adhesive joints for lighter structural components.   

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