Final answer:
Calculating the nominal fracture stress of a brittle material given its cohesive strength and crack dimensions involves engineering principles in fracture mechanics. A specific calculation method like Griffith's criterion is generally employed, but due to incomplete equation details, the precise value cannot be provided here.
Step-by-step explanation:
The problem presented involves calculating the nominal fracture stress of a brittle material with a known cohesive strength and specific dimensions of a crack. This type of calculation is commonly done in the field of materials engineering, specifically when dealing with fracture mechanics.
To solve for the nominal fracture stress, σ_φ, we would typically use the Inglis and Griffith's criterion which factors in the cohesive strength of the material, the size of the crack, and the radius of curvature at the crack tip. However, due to the lack of a full equation and given the specific values to be used, such calculation cannot be performed within this response.
The cohesive strength is a measure of the maximum stress a material can withstand while still holding together, which in this case is 25 GPa. The problem also provides the crack length (5 mm) and the radius of curvature at the crack tip (0.25 nm), which are crucial for fracture stress calculation in brittle materials.