Philipp Weißgraeber

Crack initiation in single lap joints: effects of geometrical and material properties

Brittle failure of adhesively bonded single lap joints is considered in this paper. A coupled stress and energy criterion in the framework of finite fracture mechanics is employed to study crack initiation by means of a numerical model presented by Hell et al. (Eng Fract Mech 117:112–126, 2014). Two different formulations of the coupled criterion are compared and the effect of geometrically nonlinear bending deformation of the adherends is analysed. A comparison to experimental results on the effect of the overlap length for single lap joints with composite adherends is given, showing a very good agreement of the failure load predictions. A detailed study of the effects of the geometrical and material parameters of a single lap joint configuration is given. As the energy release at crack formation is considered, the size effect of the adhesive layer thickness is covered correctly. The paper closes with an analysis of the effect of the unbonded adherend length. An approximate explicit expression for a minimum unbonded adherend length is given, which is required to optimize joint designs and to allow for the study of individual parameter effects in numerical and experimental studies.

A New Finite Fracture Mechanics Approach for Assessing the Strength of Bonded Lap Joints

For the widespread use of adhesive joints an exact and reliable prediction of the strength is mandatory. In this work, a new approach to assess the strength of single lap joints is presented. The approach is based on the hybrid criterion as postulated by Leguillon in the framework of finite fracture mechanics. It strictly combines a consideration of an energy release balance and a fulfillment of a strength criterion. The present work is based on a simple model of the joint behavior and assumptions about crack initiation. From the stress distribution of the classical shear lag theory an incremental energy release rate is derived and is used to formulate the optimization problem of the failure load. The resulting predictions of critical failure loads are compared to experimental results of single lap joints. It is shown that the new approach is able to physically describe crack formation and the corresponding critical load within the framework and limitations of the underlying assumptions and simplifications. The work closes with a discussion of the limitations and an outlook on possible improvements of the underlying models and assumptions.

Enhanced XFEM for crack deflection in multi-material joints

In this work, an enhanced eXtended finite element method (XFEM) implementation is outlined. It allows for modeling two-dimensional crack growth including potential crack deflection at significantly tougher constitutents of multi-material continua. At such material interfaces a user-defined crack deflection criterion is utilized that allows for crack deflection parallel to the interface but is also able to model crack growth that again diverges from the interface. The enhanced XFEM implementation is illustrated analyzing crack growth in a plate with two interacting inclusions showing a distinct toughening effect. Moreover, several different adhesive joint design studies are used to validate the model. The results show that the present XFEM implementation allows for an accurate strength and realistic crack pattern prediction in joint designs of complex shape, e.g. with fillets or rounded adherend corners. The given framework is general and could also be applied to the study of fracture processes including crack deflection as e.g. micro-mechanical fracture in fibre-reinforced composites or cracks around inclusions.

On the Determination of Edge Reinforcement Properties for Optimum Lightweight Design of Composite Stiffeners

In this work the determination of the properties of an edge reinforcement of a composite plate stiffener is treated. A minimum stiffness criterion for the edge reinforcement on the basis of a closed-form buckling analysis of a composite plate with edge reinforcement and elastic clamping is given. The minimum stiffness criterion is given in explicit form and in a fully dimensionless representation. A composite stiffener designed by this criterion will exhibit a local buckling mode of the web, rather than a global simultaneous buckling of both the web and the edge reinforcement. The determination of an optimum lightweight design is discussed. In an example the criterion is applied to the dimensioning of a stiffener design.