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

maximum allowable surface crack length is 1.08 mm

Step-by-step explanation:

given data

stress σ = 250 MPa

length of a surface crack = 1.6 mm

plane-strain fracture toughness = 62 MPa
`√(m)`

solution

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

`\sigm = (K)/(Y√(\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 = (K)/(Y√(\pi * a) )` ................2

so a will be here

a =
`(1)/(\pi) ( (K)/(\sigma * Y))^2`

put here value

a =
`(1)/(\pi) ( (51*√(m))/(250 * 3.49798))^2`

a = 0.001082 m

a = 1.08 mm

so maximum allowable surface crack length is 1.08 mm