**8. Conclusions and Suggestions for Future Research**

Due to the practical importance, the issues of microstructural phenomena occurring during ductile fracture of metals have been the subject of intensive research in recent years, which allows for a better phenomenon understanding and the development of advanced computational models.

Although void nucleation has been very extensively documented by the results of experimental tests and simulations, the course of ductile fracture under low triaxiality conditions, i.e., under dominant shear stress, remains an unresolved question. In this case, observations of the fracture surface microstructure indicate the presence of both large and small elongated voids. Their origins have not been fully elucidated so far, although it is believed that such void morphology results from their intensive nucleation at a late stage of deformation, prior to failure, with simultaneous growth of earlier nucleated voids. At present, there are no models of nucleation, growth, and coalescence of voids that take into account the influence of the Lode parameter, which is crucial for the course of ductile fracture under low triaxiality conditions.

As mentioned in Section 6, the stage of void coalescence is presently the least explored phase of ductile fracture. Few papers have been published in which the process of coalescence was extensively investigated in an experimental manner. This is largely due to technical difficulties, although the increasingly widely used method of microtomography seems to be a promising tool. Currently, insufficient understanding of the nature of the void coalescence phenomenon is associated with a small number of analytical models, especially in the case of the simultaneous occurrence of shear and necking of ligaments between the voids. The void coalescence models currently described in the literature are

based on certain arbitrarily accepted criteria that have not been sufficiently supported by experimental observations.

A separate problem is the identification of the model parameters. A huge number of papers have been published on this subject, but the dominant approach involves fitting the FEM simulation and the experimental results. However, this approach requires significant experimental and computational effort, and therefore it is inconvenient from a practical, engineering point of view. Moreover, the results obtained in this way apply only to samples with a specific geometry and loading method. Therefore, there is no comprehensive approach that would define standardized parameter values for typical engineering materials.

In conclusion, further research on the development of voids in metals should focus on the following aspects:


The solution of the above-mentioned problems should lead to the development of practical engineering procedures for estimating the load capacity and safety assessment of structural elements containing material microstructure defects.

**Author Contributions:** Conceptualization, W.W.; investigation, W.W.; resources, W.W.; data curation, W.W.; writing—original draft preparation, W.W.; writing—review and editing, R.P.; visualization, W.W.; supervision, W.W.; project administration, R.P.; funding acquisition, R.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** The APC was funded by Ministry of Science and Higher Education, grant number 02.0.12.00/2.01.01.00.0000, SUBB.BKWM.21.001.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** No new data were created or analyzed in this study.

**Conflicts of Interest:** The authors declare no conflict of interest.
