Topologically interlocked assemblies have traditionally been explored to study properties such as strength, toughness and fatigue when applied axial compressive load. The interlocked assemblies are used in real-life applications ranging from the aerospace industry to the construction sector. This concept is generally applied to segmented blocks to study what parameters affect failure and how the failure occurs. The Segmented interlocked assemblies are investigated to optimize performance and weight compared to a monolithic design with poor strength characteristics. Strength to weight ratio is beneficial to applications where the efficiency of the product relies heavily on the weight. This study is performed on the 3D printed cubes with interlocking geometric slots, and the segmented cubes were investigated for failure through a three-point bending test under different conditions. The study used parameters such as speed of testing, lubrication between blocks, and the shape of the slots. This paper makes use of the Taguchi design of experiments in combination with grey relational analysis to optimize the parameters. Different lubrications were used to create a variation in friction between the blocks simply. After processing the data, it was concluded that the best condition was a circle shape, with lubrication #1 at an indenter speed of 10mm/min, followed by a circle and dry at 5mm/min. Triangle shape with lubrication #1 at a speed of 5mm/min was third in terms of the overall rank. According to the results, the worst-performing condition was a circle shape with lubrication #2 at a 1mm/min speed.