Astructural 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?

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

solution

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

    ...................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 =

Y = 3.49798

so

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

    ................2

so a will be here

a =  

put here value

a =  

a = 0.001082 m

a = 1.08 mm

so maximum allowable surface crack length is 1.08 mm