Архивы рубрики ‘Mechanical Properties,. Technologies and. Economic Importance’

Mixed-Mode MI Loading (MMELS)

Figure 12 (a) shows the values of GTot (GTOt = Gj +Gjj ) obtained again by CZMs, VCCT and analytical model for the aluminum joint. The values obtained with the four methods in this case highlight a little bit the differences found for the single modes: the 3D CZM trend is almost superimposed to the […]

. Mode II Loading (ELS)

Figure 10. Comparison of (a) Gn and (b) da-dN obtained by CZM 2D, CZM 3D, VCCT 3D and analytical solution [30] in the case of ELS aluminum joints. Some differences concern the 2D CZM, that gives a trend slightly lower than the other models, and the VCCT, whose trend that is rather jagged: probably this […]

Mode I Loading (DCB)

In the case of aluminum joints, the four models show the same overall trend and an overall good correspondence with each other of the SERR plot, Figure 8 (a); in general the VCCT yields slightly lower values than the two CZM and analytical model. Moreover both the CZMs show a quite different trend in the […]


The 3D model performance is compared with the 2D version [19] concerning the value of G as a function of crack length. Due to crack front bowing (Figure 7), the average G (or Gj, Gjj) and crack length along the crack front were considered for the comparison with the 2D model. In the case of […]

Finite Element Models

The CZM fatigue debonding model was tested on various joint geometries characterised by different mixed mode ratios, in order to verify accuracy, robustness and performance in terms of computational time. In particular, pure mode I loading was simulated with a Double Cantilever Beam (DCB) geometry, pure mode II loading with an End Loaded Split (ELS) […]

Mixed Mode Loading

With the aim to extend the model to mixed-mode I/II conditions, a mixed mode cohesive law has to be defined. This is done according to the scheme shown in Figure 5 from the knowledge of the pure mode I and pure mode II cohesive laws (the index 22, refers to opening or mode I direction, […]

Finite Element Implementation

The theoretical framework described in the first section and the strain energy release rate (SERR) calculation procedures are implemented programming Fortran subroutines templates available in the commercial software Abaqus®. In particular the USDFLD Abaqus® subroutine is used to modify the cohesive element stiffness by means of a field variable that accounts for damage, while the […]

Strain Energy Release Rate Computation

The relationship between the applied strain energy release rate and the increase of damage in the cohesive zone needs a general method to calculate the value of the strain energy release rate as a function of crack length. The most common methods for the strain energy release rate evaluation by using the FEA are the […]

Model Formulation

Although, different and complicated shapes of the cohesive law are proposed in the literature, the triangular one (Figure 1) is taken as it is oftengood enough to describe crack growth behaviour. In that case, damage starts once the tripping stress Symax has been attained, decreasing progressively the element stiffness Kij. damage initiation Figure 1. Example […]

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, Italy2Centro Interdipartimentale SITEIA. PARMA, Universita di Parma, Parma, Italy Abstract 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 […]