Q6 Fracture toughness and critical crack length (8 marks)
A tensile sample of width 20 mm contains an internal crack of length 4 mm. When loaded in tension
the crack suddenly propagates when the stress reaches 450 MPa.
(a) What is the fracture toughness $K_{IC}$ of the tested material? (1 mark)
(b) If the yield strength of this material $\sigma_y = 600$ MPa, what is the critical crack length $c_{crit}$? (2 marks)
(c) If another tensile sample made of the same material with the same shape contains an internal
crack of length 2 mm. Will it fail by yielding or by fast crack propagation? (2 marks)
Hint: Fracture toughness $K_{IC} = Y\sigma_f\sqrt{\pi c}$, where $\sigma_f$ is the fracture strength
and c is half length of the internal crack. Assume the geometric factor Y = 1.
The critical crack length $c_{crit} = \frac{\sigma^2}{\pi K_{IC}^2}$.
(d) Matching the materials properties with their descriptions (3 marks)
Fracture toughness
Yield strength
Young's modulus
the ability to resist plastic deformation
the ability to resist elastic deflection
the ability to resist fast crack propagation
