# Prediction of the Crack Front Shape of the Corner Interface Crack
## 4 Conclusions  
In this comprehensive research endeavor, we meticulously examined the intricate growth patterns of an interface crack originating at a right-angle corner and progressing along the plane where the two dissimilar material plates are conjoined. The study takes a nuanced approach by exploring the diverse geometrical formations of the crack front, encompassing concave, triangular, and convex shapes. These variations in crack front geometry are pivotal to understanding how they influence and modulate the crack propagation process.  
To unravel the underlying mechanisms governing the crack growth, we employ the modified Paris's law, a mathematical framework well-suited for analyzing the growth behavior of angular interface cracks under mixed mode conditions. This analytical tool  
Figure 7: The propagation of the interfacial corner crack for the bimaterial combination silicon/epoxy. (**a**) Concave crack front, (**b**) triangular crack front, (**c**) convex crack front.  
enables us to discern critical thresholds where stress intensity factors and fracture toughness interact, delineating the stability of different crack front shapes.  
Our investigation vividly illustrates the evolution of the crack front for the three distinct shapes--concave, triangular, and convex--at the interface between Al\({}_{2}\)O\({}_{3}\) and steel. By closely examining the crack advancement patterns, we arrive at a noteworthy and consistent conclusion across various material combinations. The results unequivocally affirm the stability of the triangular crack shape, presenting it as the most structurally sound and predictable configuration.  
This profound revelation has far-reaching implications. Armed with a deep comprehension of the bimaterial combination parameters and crack front geometry, we gain the remarkable ability to foresee and ascertain the most stable crack front shape in a given scenario. This predictive capacity is a powerful tool in engineering and material science, guiding the design and construction of structures with enhanced durability and structural resilience. It lays the foundation for advancements in various domains, ensuring safer and more reliable material utilization in critical applications.  
The simulation and calculations in this article were conducted by application of the _Mathematica_[9] symbolic programming routine. The results are then presented in the form of graphs from which it was concluded which of the three shapes of the crack front is the most stable one, i.e., which one would not change to any of the other two shapes during the crack propagation. This type of problem is interesting for the further study and should involve considering different variations of the bi-material combinations to prevent a delamination of the stratified materials, in the first place.  
Conceptualization, J.M.D. and R.R.N.; methodology, R.R.N.; software, J.M.D.; validation, R.U.; formal analysis, J.M.D. and J.P.; resources, R.U.; data curation, J.M.D.; writing--original draft preparation, J.M.D. and R.R.N.; writing--review and editing, R.R.N.; visualization, J.M.D. and R.R.N.; supervision, R.U.; project administration, J.P.; funding acquisition, R.U. All authors have read and agreed to the published version of the manuscript.  
This research was partially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, within the funding of the scientific research work at the University of Belgrade, Technical Faculty in Bor, contract number 451-03-47/2023-01/200131 and the project \"Support of research and development capacities to generate advanced software tools designed to increase the resilience of economic entities against excessive volatility of the energy commodity market\", of Operational Programme Integrated Infrastructure, number ITMS2014+ code 313011 BUK9, co-funded by the European Regional Development Fund.  
Not applicable.  
Data are contained within the article.  
The authors declare no conflict of interest.