In-plane thermo-elastic constants of symmetric damaged laminates containing transverse cracks in plies and local delaminations starting from crack tip are predicted using a crack opening (COD) and crack sliding displacement (CSD) based approach. An exact elastic analysis shows that the displacement gap on the delamination crack surfaces does not enter the stiffness expressions explicitly. The delamination affects the stiffness via larger COD and CSD of the intralaminar crack. This means that the same expressions for cracked laminates with and without delaminations can be used but with different expressions for COD and CSD. Finite element method is used to analyze the CSD dependence on delamination length and crack density. The obtained approximative expressions for CSD are in a good agreement with FEM. It is shown that in cases when it depends on CSD only, the predicted shear modulus of laminates is in an excellent agreement with direct FEM calculations. The used homogenization over couples of off-axis plies (monoclinic materials) in CSD expressions for balanced laminates is validated.

Structural battery composites require a structural electrolyte to work. The structural battery electrolyte has a bicontinuous microstructure which enables its dual roles: mechanical load transfer and ion transport between the electrodes. These structural electrolytes are difficult to characterise mechanically via bulk tests. For this reason, no extensive characterisation of the mechanical properties of the structural battery electrolyte has been performed to date. In this study, we highlight the many challenges of these types of tests, including the complexity of sample manufacturing, preparation and testing. We further demonstrate a method to prepare test samples and to perform mechanical tests on the structural battery electrolyte. The executed test campaign provides measures of Young's modulus (approximately 412 MPa) and Poisson's ratio (0.34), as well as tensile (4.85 MPa) and compressive strength (32.66 MPa) and strain to failure (2.49 % and 28.11 % in tension and compression, respectively). In addition, cure shrinkage is investigated and found insignificant. These results are crucial for the further development of structural battery composites as they allow for accurate prediction of their internal stress states.

Usually, the viscoelastic (VE) response of polymers for applications in composites is obtained in uniaxial strainor stress-controlled tests. However, analyzing multimaterial structures by the Finite Element Method (FEM) or by other numerical or analytical tools, a material model in terms of a complete set of compliance functions and/or relaxation functions is required. In this paper, a methodology and exact analytical expressions for calculating the whole set of VE functions is presented based on the relaxation modulus E(t)and Poisson’s ratio v (t) determined in strain-controlled tests. The method is based on Laplace transforms, where an exact inversion is possible if a linear VE model with functions in Prony series is used. Results of the analytical model are compared with the FEM simulation, where specific boundary conditions to determine each particular VE function are used. Finally, the applicability of the so-called quasi-elastic method is investigated, where the expressions of elasticity theory are used to calculate a given viscoelastic function at an instant of time tk using the instant values of E(tk) and v(tk). For isotropic materials, the three approaches render almost coinciding results.

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.   

An alternative to traditional fracture mechanics methodology to predict direction for crack propagation in the adhesive layer of bonded stiff materials is demonstrated. The approach is based on the analysis of the location of maximum of the hoop stress in relation to the existing crack tip. Such method is very convenient and fast as it does not require a lot of computational resources and is easy to implement compared to other known numerical methods dealing with similar problems (e.g. X-FEM). The method is validated by fracture mechanics approach using energy release rate to predict crack propagation direction. The verification is done by using bi-material DCB specimen with relatively thick adhesive layer as an example.

After proving the applicability of the maximum hoop stress criterion the parametric study on factors affecting crack propagation in the adhesive layer is carried out. Such parameters as bending stiffness of beams, thickness of the adhesive layer, distance to the bond-line, length of the initial pre-crack are analyzed.

A numerical study for the double-lap adhesive joint made of similar adherends subjected to tensile and thermal loads is presented. A novel displacement coupling conditions which are able to correctly represent monoclinic materials (off-axis layers of composite laminates) are used to build a comprehensive numerical model. Two types of double-lap joints are considered in this study: metal–metal and composite-composite. In case of composite laminates, four lay-ups are evaluated: unidirectional ([0₈]_T and [90₈]_T) and quasi-isotropic laminates ([0/45/90/−45]_S and [90/45/0/−45]_S). The effect of different parameters (adherend stiffness, ply stacking sequence, adherend thickness, one-step or two-step manufacturing of the joint) on peel and shear stress distribution in the middle of the adhesive is studied. The comparison of the behaviour of single-lap and double-lap joint in relation to these parameters is made. The maximum peel and shear stress at the ends of the overlap with respect to the axial modulus of the adherends are presented in a form of the master curves. The analyses of results show that: the maximum peel and shear stress concentration at the overlap ends is reduced with the increase of the axial modulus of the adherend; the stress distribution in the adhesive layer can be improved (lower stress concentrations and level-out the curve) by changing the fibre orientation (which affect the stiffness) in plies connected to the adhesive layer.

A comprehensive stress analysis by means of Finite Element Method (FEM) for single-lap joint subjected to thermal and mechanical loads is presented in this paper. Simulation is used to predict the effect of residual thermal stresses (caused by difference of temperature of use and elevated temperature during the assembly of the joint) on stress distribution within adhesive layer. The residual thermal stresses are assigned to joint members as initial condition before the mechanical load is applied. The FEM model employs linear and nonlinear material model and accounts for geometrical nonlinearity. It is confirmed that the difference between the manufacturing and the ambient temperature results in high residual thermal stresses, especially in axial and lateral directions of the joint. The calculation of total stress as superposition of thermal and mechanical stresses works only for linear materials. Moreover, simultaneous application of temperature and mechanical load (applied strain in case of displacement controlled test) in FEM produces inaccurate results, since in real situation the strain is applied to already thermally loaded structure. It is also found that the residual thermal stresses may reduce the peel and shear stress concentration in the adhesive at the ends of overlap and the shear stress within the overlap.

The objective of this work is to evaluate the effect of residual thermal stresses, arising after assembling a single-lap joint at elevated temperature, on the inelastic thermo-mechanical stress state in the adhesive layer. The numerical analysis (FEM) employing linear and non-linear material models, with geometrical nonlinearity accounted for, is carried out. Simulating the mechanical response, the calculated thermal stresses are assigned as initial conditions to polymeric, composite and metallic joint members to reflect the loading sequence where the mechanical strain is applied to cooled-down structure. It is shown that the sequence of application matters and simulations with simultaneous application of temperature and strain give different result. Two scenarios for adhesive joints with composites are studied: joining by adhesive curing of already cured composite parts (two-step process) and curing the adhesive and the composite simultaneously in one-step (co-curing). Results show that while in-plane stresses in the adhesive are higher, the peaks of out-of-plane shear stress and peel stress (most responsible for the joint failure) at the end of the overlap are reduced due to thermal effects. In joints containing composite parts, the one-step joining scenario is more favorable than the two-step. The ply stacking sequence in the composite has significant effect on stress concentrations as well as on the plateau value of the shear stress in the adhesive.

A numerical study of the adhesive joint made of similar and dissimilar adherends subjected to thermo-mechanical loading is presented. A comprehensive numerical model was used for this purpose with the novel displacement coupling conditions which are able to correctly represent monoclinic materials (off-axis layers of composite laminates). The geometrical nonlinearity as well as nonlinear material model are also taken into account. Three different types of single-lap and double-lap adhesive joints are considered in this study: a) metal-metal; b) composite-composite; c) composite-metal. In case of composite laminates, four lay-ups are evaluated: uni-directional ([0₈]_T and [90₈]_T) and quasi-isotropic laminates ([0/45/90/-45]_S and [90/45/0/-45]_S). This paper focuses on the parameters which have the major effect on the peel and shear stress distribution within adhesive layer at the overlap ends. The comparison of behaviour of single- and double- lap joints in relation to these parameters is made. The master curves for maximum stress (peel and shear) at the ends of the overlap with respect to the bending stiffness and axial modulus of the adherends are constructed by analysing stress distributions in the middle of the adhesive. The main conclusions of this paper are: the maximum peel stress value for SLJ is reduced with increase of the adherend bending stiffness and for DLJ, similar behaviour was observed at the end next to the inner plate corner, while, at the end next to the outer plate corner peel stress is reduced with increase of adherend axial modulus.

This study presents comprehensive numerical stress analysis in the adhesive layer of a single-lap joint subjected to various loading scenarios (mechanical and thermal loading). For this purpose numerical model (finite element method) with novel displacement coupling conditions able to correctly represent monoclinic materials (off-axis layers of composite laminates) has been developed. This model includes nonlinear material model and geometrical nonlinearity is also accounted for. The effect of thermal residual stresses (in adhesive) is analysed for various methods of manufacturing of single lap joint. The sequences of application of thermal and mechanical loads for the analysis of the thermal residual stresses in joints are proposed. It is shown that the most common approach used in many studies of linear superposition of thermal and mechanical stresses works well only for linear materials and produces wrong results if material is non-linear. The present study demonstrates suitable method to apply combined thermal and mechanical loads to get accurate stress distributions. Based on the analysis of these stress distributions the conclusions concerning the effect of the thermal residual stresses on peel and shear stress concentrations are made. The comparison between effect of thermal stresses in case of the one-step and two-step joint manufacturing techniques is made.