Question

A structural component is fabricated from an alloy that has a plane-strain fracture toughness of 62 MPa1m. It has been determined that this component fails at a stress of 250 MPa when the maximum length of a surface crack is 1.6 mm. What is the maximum allowable surface crack length (in mm) without fracture for this same component exposed to a stress of 250 MPa and made from another alloy with a plane-strain fracture toughness of 51 MPa1m?

Answer 1

Answer:

maximum allowable surface crack length is 1.08 mm

Explanation:

given data

stress σ = 250 MPa

length of a surface crack = 1.6 mm

plane-strain fracture toughness = 62 MPa $\sqrt{m}$

solution

we will calculate here design parameter by design stress equation that is

$\sigm = \frac{K}{Y\sqrt{\pi * a} }$     ...................1

here σ is stress given 250 and a is length of a surface crack and K is plane strain fracture toughness so Y will be here

250 = $\frac{250}{Y*\sqrt{\pi * 1.6*10^{-3}} }$

Y = 3.49798

so

now we find maximum allowable surface crack length for another alloy using relation

$\sigm = \frac{K}{Y\sqrt{\pi * a} }$     ................2

so a will be here

a = $\frac{1}{\pi} ( \frac{K}{\sigma * Y})^2$  

put here value

a = $\frac{1}{\pi} ( \frac{51*\sqrt{m}}{250 * 3.49798})^2$  

a = 0.001082 m

a = 1.08 mm

so maximum allowable surface crack length is 1.08 mm