A self-adaptive cohesive zone model for interfacial delamination

Abstract

Interfacial failure in the form of delamination, often results in malfunction or failure of laminated structures. Different numerical approaches have been proposed for the simulation of this process. Due to the appealing feature of predicting both the delamination onset and its growth, cohesive zone models have been widely used to simulate delamination as a result of a gradual degradation of the adhesion between two materials when they become separated. Application of cohesive zone models for the modelling of delamination in brittle interfaces in a quasi-static finite element framework suffers froman intrinsic discretization sensitivity. A large number of interface elements are needed for the discretization of the process zone of a cohesive crack. Otherwise, a sudden release of energy in large cohesive zone elements results in a sequence of snap-through or snap-back points to appear in the global load-displacement response of the system which compromises the numerical efficiency. While computationally expensive path-following techniques can be used to follow the oscillatory path, the efficiency and robustness of brittle cohesive zone models can be significantly increased by reducing the oscillations observed in the global load-displacement behaviour without a further mesh refinement. In line with this purpose, the separation approximation in the process zone is enriched with an adaptive hierarchical extension. The linear separation approximation throughout the cohesive zone element is enriched with a bi-linear function, where the enrichment peak position and the magnitude of the enrichment are regarded as additional degrees of freedom obtained by minimization of the total potential of the global system. The mobility of the peak of the enrichment function within individual cohesive zone elements locally adapts the discretization to the physics governing the problem. Important numerical aspects of the proposed enrichment strategy such as its mobility and uniqueness have been thoroughly investigated while its limitations are addressed. The efficiency and robustness of the enrichment are shown through numerical examples which prove the general applicability of the methodology. In fact, application of the elaborated enrichment eliminates the need for a further mesh refinement while keeping the standard Newton-Raphson approach applicable in the case of a relatively coarse mesh which saves considerable computational costs. Extension of the proposed enrichment scheme to delamination in a threedimensional finite element framework has been carried out as well. Planar interix face elements have been enriched along all edges by bi-linear functions with mobile peaks. The effect of the proposed methodology on reducing discretization-induced oscillations is quantitatively evaluated. To deal with planar crack growth where the crack front is oblique with respect to element edges, a non-hierarchical enrichment strategy is also developed and its performance is compared with its hierarchical counterpart. The self-adaptive finite element formulation is extended to a framework suitable for large deformations and is applied to interfaces in microelectronics under realistic mixed-mode loading conditions. In particular, the material/interface systems used in miniaturized mixed-mode bending tests, which are conducted for a wide range of mode angles, are modelled to make a direct comparison with experimental results. The interface constitutive lawthat is used takes the dependence of fracture toughness on mode-mixity into account. Thereby, the enhanced cohesive zone model can be used for the simulation of the behaviour of brittle interfaces in an accurate, effective, and efficient manner