Answer:
Yes, fracture will occur since toughness (42.4 MPa) is greater than the toughness of the material, 40MPa
Explanation:
Given
Toughness, k = 40Mpa
Stress, σ = 300Mpa
Length, l = 4mm = 4 * 10^-3m
Under which fracture occurred (i.e., σ= 300 MPa and 2a= 4.0 mm), first we solve for parameter Y (The dimensionless parameter)
Y = k/(σπ√a)
Where a = ½ of the length in metres
Y = 40/(300 * π * √(4/2 * 10^-3))
Y = 1.68 ---- Approximated
To check if fracture will occur of not; we apply the same formula.
Y = k/(σπ√a)
Then we solve for k, where
σ = 260Mpa and a = ½ * 6 * 10^-3
So,.we have
1.68 = k/(260 * π * √(6*10^-3)/2)
k = 1.68 * (260 * π * (6*10^-3)/2)
k = 42.4 MPa --- Approximately
Therefore, fracture will occur since toughness (42.4 MPa) is greater than the toughness of the material, 40 MPa
