A series of crack growth tests on an aluminium alloy under c

A series of crack growth tests on an aluminium alloy under cyclic stresses gave the following empirical relationship: da/dN = 4 times 10^-11 [DeltaK]^3.54 where da/dN has the unit of m/cycle and DeltaK has the unit of MPa m^1/2. The fracture toughness of the aluminium alloy is 35 MPa m^1/2. Discs manufactured from the aluminium alloy are used in the rotor assembly of a gas turbine. During assembly of the system a scratch is made on the surface of the disc. The rotation of the turbine blades cause a maximum stress of 350 MPa, perpendicular to the plane of the scratch causing it to open, and the minimum stress can be assumed as zero. The plastic zone correction can be ignored. (i) If the depth of the scratch is 0.1 mm, calculate the number of cycles that the aluminium alloy disc can withstand before failure. (ii) Determine the depth of the scratch that will allow the aluminium alloy disc to undergo atleast 2000 cycles in service.

Solution

(i) 3117 cycles. (ii) 0.168mm