A meso-mechanical finite element model for a thin adhesive layer is developed. The model is calibrated to experimental results where the adhesive layer is loaded in monotonically increasing peel or shear, cf. Andersson and Stigh [1] and Alfredsson et al. [2], and to an in situ SEM study of the fracture process. The purpose of the meso-mechanical finite element model is to facilitate the development of constitutive laws for adhesive layers.
Ideas developed by Needleman [3], where structural continuum elements are bonded by cohesive elements are used as a basis for the finite element mesh. This thus enables micro cracks to propagate along the finite element boundaries.
The simulations are found to be in good agreement with the experiments. The model is also capable of reproducing realistically the deformation observed in both peel [1] and shear [2] experiments.
A finite element modle of a double cantilever beam specimen is developed. The adherents are modeled using plane strain elastic continuum elements. Furthermore, the adhesive is modeled using a mesomechanical modeling teqnique wich allows for simulation of initiation and prognationb of micro-cracks. This enables the modelling of entire process of degradation and fracture of the adhesive layer. The purpose of the present study is to compare the stress-deformation behavior in an idealized peel loading to the behavior in a double cantilever beam (DCB) specimen where the adhesive layer is deformed wilt a slight gradient along the layer. Previously performed experiments and simulations of the RVE are used as a compariosn to the simulated results.
The purpose of this work is to develop a flexible cohesive law to simulate the constitutive behaviour of an adhesive layer under mixed mode loading. A mixed mode cohesive law that captures the linear elastic and softening behaviour before fracture is presented. This simple model uses a coupled formulation to describe the mixed mode cohesive behaviour. It also allows for different fracture parameters, such as fracture energy, strength and critical separation in different mode mixities. Thus, the fracture process in mode I (peel), in mode II (shear) or in mixed mode (a combination of peel and shear) can be modelled without the usual constraint of a common fracture energy in peel and shear. Examples are given of FE-implementation of the normalised cohesive law, namely for the Unsymmetric Double Cantilever Beam (UDCB) specimen and the Mixed-mode double Cantilever Beam (MCB) specimen. Both specimens are adhesively bonded and loaded in mixed-mode.
This thesis is concerned with the modeling, simulation and analysis of adhesive layers. By use of an in situ scanning electron microscopy study it is found that the adhesive studied in the present thesis has a very complex structure with two different compounds, a mineral and an epoxy/thermoplastic blend. A representative volume element (RVE) model is developed to study the behavior of the adhesive layer at the meso-level. It is a continuum model where interface finite elements are implemented at the boundaries of the continuum elements in order to enable crack initiation and propagation of micro cracks. On a structural level, two deformation modes, modes I and II, dominate the behavior of thin adhesive layers. With the RVE it is possible reproduce experimental stress-deformation relations from both modes. However, in a real structure, mixed mode loading usually occur. A range of mode mixes is studied, using the RVE, from an un-loaded state until fracture of the layer. The results indicate that the behavior of the interface elements dominate for mode mixes close to mode I and plasticity in the continuum elements dominates for mode II dominated mode mixes. Furthermore, effects of large root curvatures of the adherends is analyzed numerically by simulating plastically deforming double cantilever beam specimens using the finite element model. The developed RVE is implemented in the models to simulate the behavior of the adhesive layer. By this methodology, virtual experiments can be analyzed with extreme detail. It is shown that in-plane straining of the adhesive layer significantly influences the strength of adhesive joints at large plastic strain of the adherends. There is a never ending need in industries to minimize computational time. To this end, an interphase finite element for structural analyses is developed. The element considers in-plane straining of the adhesive layer due to large curvatures of surrounding substrates.
A thin adhesive layer is analyzed using a representative volume element (RVE). The RVE is comprised by, both continuum and interfacial finite elements. The interface elements allow for crack initiation and crack propagation. To obtain realistic results from the RVE simulation, an in situ scanning electron microscopy (SEM) study is performed. Results from the SEM study show that the adhesive has a very complex structure with two different compounds, a mineral and an epoxy/thermoplastic blend.
The RVE is subjected to two different load cases, peel and shear. An evolutionary algorithm is used to calibrate the numerical model to experimental results. The simulation results are compared to experimental results to verify the numerical model. The simulations show good agreement with the experimental results for both the peel and shear experiments.
A representative volume element is modeled using the finite element method. It is used to analyze mixed mode behavior of a thin adhesive layer. Two sources of dissipation is modeled; plasticity and decohesion. Macroscopic traction–separation laws are extracted from the simulations. The results indicate that a boundary of mode mix exists between a region where major plastic dissipation is present and a region where it is not. Without major plastic dissipation, the fracture energy is low and essentially governed by the cohesive properties. This is the case in peel dominated loading cases. In shear dominated loading cases plastic dissipation gives a substantial contribution to the fracture energy. The results show that pure shear loading gives the largest fracture energy.
A mesomechanical finite element model of a thin adhesive layer is developed. The model is calibrated to previously performed experiments. In these, the adhesive layer is loaded in monotonically increasing peel or shear. An in situ SEM study is also performed and used to guide the modeling and calibration. The purpose of the mesomechanical finite element model is to facilitate the development of constitutive laws for adhesive layers. The modeling is based on Xu and Needleman’s method where all continuum finite elements are surrounded by interface elements that allow for the development of micro cracks. Thus, this enables the modeling of the entire process of degradation and fracture of the adhesive layer. A genetic algorithm is developed for the calibration. The simulations show good agreement with the experiments.
A weighted potential methodology is developed by utilizing pure mode I and mode II energy release rate experiments to determine the traction-separation relations for thin adhesive layers. The experimentally measured energy release rates act as boundary conditions for developing a weighted potential function. Thus, the tractions for any mixed mode loading can be established. Changes of mode mix during an experiment can also be captured by the law since every mixed mode variation is given by the potential function. Furthermore, by use of an inverse J-integral approach and damage type variables, the traction-separation relations for any mode mix can be approximated by use of pure mode experiments. Numerical simulations show the applicability of the methodology. The results indicate that the methodology is promising when simulating the constitutive behavior of adhesive layers.
A special purpose finite element is developed for structural simulations of complex adhesively bonded structures. In the interphase element, the adhesive is explicitly regarded as a material phase between two substrates. The element considers large rotations. Furthermore. it considers in-plane straining of the adhesive due to large curvatures of the bonded shells. This feature appears especially important when considering bonding of thin plastically deforming metallic shell structures. Simulations are made on specimens where the adherends deform both elastically and plastically. The results are in good agreement with previously performed experiments. Copyright (0 2008 John Wiley & Sons, Ltd.
A detailed model of experiments with the double cantilever beam specimen is set up. Analysis of the model shows that an experimentally deduced apparent increase of fracture energy with severely deforming adherends is due to contributions of in-plane straining of the adhesive layer to the fracture energy. An analysis with the J-integral confirms the result.
An overview of recent development of cohesive modelling is given. Cohesive models are discussed in general and specifically for the modelling of adhesive layers. It is argued that most cohesive models model a material volume and not a surface. Detailed microscopic and mesomechanical studies of the fracture process of an engineering epoxy are discussed. These studies show how plasticity on the mesomechanical length scale contributes to the fracture energy in shear dominated load cases. Methods to measure cohesive laws are presented in a general setting. Conclusions and conjectures based on experimental and mesomechanical studies are presented. The influence of temperature and strain rate on the peak stress and fracture energy of cohesive laws indicates fundamentally different mechanisms responsible for these properties. Experiments and mesomechanical studies show that in-plane straining of an adhesive layer can give large contributions to the registered fracture energy. Finite element formulations including a method to incorporate this influence are discussed.