Final answer:
A material fatigue failure diagram represents the relationship between stress amplitude and the number of cycles to failure. For brittle materials like cast iron, crack initiation and propagation can result in failure. The diagram typically includes an endurance limit and a fatigue limit.
Step-by-step explanation:
A material fatigue failure diagram represents the relationship between the stress amplitude and the number of cycles to failure for a particular material. In the case of bending loads, the stress amplitude can be calculated using the equation σ_a = (S_max - S_min)/2, where S_max is the maximum stress and S_min is the minimum stress in the bending cycle.
For a brittle material like cast iron, the stress concentration at the surface of the part can lead to crack initiation and propagation, resulting in failure. In the fatigue failure diagram, the stress amplitude is plotted on the y-axis and the number of cycles to failure is plotted on the x-axis. The curve typically shows an endurance limit, below which the material can withstand an unlimited number of cycles without failure, and a fatigue limit, above which failure will occur even with a small number of cycles.
In this case, the material properties for cast iron are given as S_ut = 345 MPa (ultimate tensile strength), S_10³ = 310.5 MPa (fatigue strength at 1000 cycles), and S_10⁸ = 121 MPa (fatigue strength at 100 million cycles). Using these values, you can sketch the appropriate material fatigue failure diagram for casting subjected to bending loads.