Answer
$σ_{c} = 134 MPa$
Work Step by Step
Given:
Suppose that a wing component on an aircraft is fabricated from an aluminum alloy that has a plane-strain fracture toughness of $26.0 MPa \sqrt m (23.7 ksi \sqrt in.)$. It has been determined that fracture results at a stress of 112 MPa (16,240 psi) when the maximum internal crack length is 8.6 mm (0.34 in.)
Required:
compute the stress level at which fracture will occur for a critical internal crack length of 6.0 mm (0.24 in.)
Solution:
Using Equation 8.5, compute the parameter $Y$:
$Y = \frac{K_{Ic}}{σ\sqrt πa} = \frac{26.0 MPa \sqrt m}{(112 MPa)\sqrt (π)(\frac{8.6 \times 10^{-3} mm}{2})} = 2.00 $
Using Equation 8.6, we find:
$σ_{c} = \frac{K_{Ic}}{Y\sqrt πa} = \frac{26.0 MPa \sqrt m}{(2.00)\sqrt (π)(\frac{6.0 \times 10^{-3} mm}{2})} = 134 MPa$