The study presented in this paper was undertaken in response to two instances of unexpected blade breakage in the cutting blade used in a Carton Wrap machine (CW). Failure of the Al7075 alloy blade occurred at an indentation during typical operational loading conditions. Subsequent metallographic examinations of the fractured samples confirmed that both cases were attributed to fatigue failure. The main objective of this study is to investigate potential causes of fatigue failure in the CW blade using simplified linear elastic static numerical simulations through Finite Element Analysis (FEA). In this research, we employed the well-established Theory of Critical Distance (TCD), and this case study provided a contextualization at an industrial level. Furthermore, the analysis focused on a second key aspect: proposing a new blade geometry aimed at mitigating the identified issues and eliminating possible causes of failure. In this context, the actual stress concentration at the indentation was determined using the TCD with Line Method (LM). The results from the numerical simulations indicated that the new blade geometry significantly reduced stress concentration, resulting in a risk factor reduction of approximately four compared to the original blade design, even under non-optimal operating conditions. Overall, in conjunction with simple linear static FEA, the proposed numerical approach provided substantial support for designers, especially in fault analysis and when comparing different industrial solutions.