Answer:
We are to determine the stress level at which a component of an aircraft will fracture for a given strain fracture toughness (35MPa ) and maximum internal crack length (2.19 mm) and the stress level is 221MPa, given that fracture occurs for the same component using the same alloy at another stress level (365 MPa) and another internal crack length (1.10 mm).
The crack modulus Y for the conditions under which fracture occurred must be determined, as follows,
Y[tex]\Y =\frac{K}{\alpha \sqrt{\pi a} }[/tex]
where,
K1 = strain fracture toughness = 35MPa
α1 = stress level = 221MPa
a1 = half of the max internal cracked length = 2.19mm/2 = 1.095x10⁻³m
Y = 35 MPa / (221MPa (√π x 1.095x10⁻³))
Y = 2.7
Since Y=2.7, we can now find the new strain fracture toughness for the new stress level and internal cracked length (331MPa and 1.1mm)
as follows,
K = Yα√πa
K = 2.7 x 331MPa x (√π x 0.55x10⁻³)
K = 37.15MPa
The value of the new fracture toughnes is 37MPa
