A structural component in the shape of a flat plate 24.2 mm thick is to be fabricated from a metal alloy for which the yield strength and plane strain fracture toughness values are 545 MPa and 20.0 MPa-m1/2, respectively. For this particular geometry, the value of Y is 1.0. Assuming a design stress of 0.2 times the yield strength, calculate the critical length of a surface flaw.

ac = 0.01071 m = 10.71 mm

Explanation:

Given:-

- The thickness of plate, t = 24.2 mm

- The yield strength of metal alloy, σy = 545 MPa

- The fracture toughness, Kic = 20.0 MPa-√m

- The geometrical criticality, Y = 1.0

- Factor of design, nd = 0.2

Find:-

Calculate the critical length of a surface flaw

Solution:-

- We are to determine the minimum critical length (ac) for the design stress (σd) that leads to failure of the plate with thickness (t).

- The relation for the critical length (ac) depends on the material intrinsic properties i. e Fracture toughness - (Energy required for the material to fracture) and the design yield strength (σd = nd*σy).

- The relation is given below:

ac = [ Kic / Y*σd ] ^2 * (1 / π)

ac = [ Kic / Y*σy*nd ] ^2 * (1 / π)

ac = [ 20.0*5 / 1*545 ] ^2 * (1 / π)

ac = 0.01071 m = 10.71 mm

Answer: The minimum critical length (ac) for the metal alloy subjected to the given design stress is (10.71 mm) for fracture.