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 VCCT trend, while the analytical solution gives a slight overestimation and the 2D CZM a slight underestimation with respect to the previous ones.

These differences become larger in the crack length vs. number of cycles plot (Figure 12 (b)), where again CZM 3D and VCCT give similar result, while analytical solution and the 2D CZM give respectively higher and lower crack growth rate. Figure 12 (c) shows the variation of the mixed mode ratio (MM) during the propagation. For the four models, the trend is quite similar and almost constant close of a value of 0.4. Only in the VCCT model the MM value results quite higher than the other (the differences in the order of 9%). In the case of composite joints (Figure 13) the three models give quite different results: although the trends of the total strain energy release rate (GTOT=Gj+Gjj) are similar (Figure 13 (a)), the mode separation produces differences of the mixed mode ratio in the order of 30% (Figure 13 (c)), and this, in turn, produces significant differences in terms of crack length vs. number of cycles prediction (Figure 13 (b)). This phenomenon, still under investigation, is thought to be produced by the material anisotropy.


The performances of the 3D CZM model were compared with a previously developed 2D model and analytical solutions on mode I, mode II and mixed-mode I/II loaded cracks in bonded aluminum or composite assemblies. The results are in an overall good agreement with each other, with the exception of the first instants of propagation of the 3D model, where the CZM process zone has to shape up. Next step should to assess this initial transient of 3D process zone formation, leading to a higher predicted number of cycles with respect to 2D simulation, by experimental evidence.


The work of F. Moroni was partially supported by Emilia-Romagna

Region (POR FSE 2007-2013).


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