Three-Dimensional vs. Two-. Dimensional Modelling of Fatigue. Debonding or Delamination Using. Cohesive Zone

A. Pirondi1’ * G. Giuliese1 and F. Moroni2

:Dipartimento di Ingegneria Industriale,

Universita di Parma, Parma, Italy
2Centro Interdipartimentale SITEIA. PARMA,

Universita di Parma, Parma, Italy


Adhesively bonded metallic and/or composite material structures are present as principal structural elements in several fields, such as aeronautics, automotive, nautical and wind energy. A numerical method able to reproduce three-dimensionally the fatigue debonding/delamination evolution in bonded structures is therefore necessary to improve their performances.

In this work the cohesive zone model previously developed by the authors to simulate fatigue crack growth at interfaces in 2D geometries is extended to 3D cracks under mixed-mode I/II loading.

Corresponding Author address: Email:alessandro. pirondi@unipr. it.

Keywords: Fatigue, cohesive zone, finite element analysis


Composite and hybrid metal/composite structures are nowadays present not only in the aerospace industry, but thanks to continuous performance improvement and cost reduction, also many more industrial fields are approaching the use of multimaterial structural elements. This requires, in turn, extensive use of adhesive bonding and a more and more sophisticated capability to simulate and predict the strength of bonded connections where, for this purpose, analytical methods are being progressively integrated or replaced by Finite Element Analysis (FEA). In engineering applications, it is well established that fatigue is the root cause of many structural failures. In the case of bonded joints, fatigue life is related to the initiation and propagation of defects starting at free edges of joining regions or other features, such as through-thickness holes. In the case of composite or metal/composite joints, fatigue can start also from defects at the same locations cited above, with the difference that the crack may either run into the adhesive or become a delamination crack. Especially in the case of damage tolerant or fail safe design, it is necessary to know how cracks, or in general defects, propagate during the service life of a component. A numerical method able to reproduce three-dimensionally the fatigue debonding in structures is therefore necessary to improve their performances.

The relationship between the applied stress intensity factor and the fatigue crack growth (FCG) rate of a defect is generally expressed as a power law [1]. In the case of polymers, adhesives and composites, the relationship is traditionally written as a function of the range of strain energy release rate (AG) as

Подпись: (1)— = BAGd dN

where B and d are parameters depending on the material and load mixity ratio, and a is the defect length. In this simple form, the presence of a fatigue crack growth threshold and an upper limit to AG for fracture are not represented although, when needed, expressions accounting for these limits can be easily found (see for example [2]). In the same way, the influence of the stress ratio,

R, on the fatigue crack growth rate can be introduced into Eq.(1) by a term derived from extensions of the Paris law expressed in terms of the range of stress intensity factor, AK [3].

When a solution for the strain energy release rate as a function of crack length exists, then the number of cycles to failure comes out from the numerical integration between the initial crack length (a0) and the final crack length (af) of the inverse of Eq.(1) ([2], [4]).

When a theoretical solution for the strain energy release rate does not exist, Finite Element (FE) simulation is commonly used to compute it. The prediction of crack growth can be then carried out by a stepwise analysis, each step corresponding to a user-defined crack growth increment and the number of cycles is obtained by integrating the crack growth rate computed from the Paris law. To speed up the process, in some finite element softwares, this procedure is integrated in special features (for example the *Debonding procedure in Abaqus®, Dassault Systemes, Paris, France), where the strain energy release rate is obtained using the Virtual Crack Closure Technique (VCCT). An alternative way for dealing with fatigue crack growth problems is using the cohesive zone model (CZM). This model is commonly used for the simulation of the quasi static fracture problems, especially in the case of interface cracks such as in bonded joints and delamination in composites ([5]- [7] among others). The possibility to simulate the growth of a crack without any remeshing requirements and the relatively easy possibility to manipulate the constitutive law of the cohesive elements makes the cohesive zone model attractive also for the fatigue crack growth simulation [8]-[19]. However, differently from VCCT, three-dimensional fatigue debonding/delamination with CZM is not yet state-of-art in finite element softwares. Using [12] as a reference, but modifying the damage definition, including an automatic strain energy release rate evaluation and introducing different mixed mode criteria for the computation of the fatigue crack growth rate, the authors developed a model able to correctly predict fatigue crack growth at interfaces in two­dimensional geometries [19]. The extension of the model to full 3D cracks undergoing mixed-mode I/II fatigue loading is presented in this work, with a special emphasis on the changes done with respect to the 2D model.

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