Question

A structural component is fabricated from an alloy that has a plane strain fracture toughness of 45 MPa.m1/2. It has been determined that this component fails at a stress of 300 MPa when the maximum length of a surface crack is 0.95 mm. What is the maximum allowable surface crack length (in mm) without fracture for this same component exposed to a stress of 300 MPa and made from another alloy with a plane-strain fracture toughness of 57.5 MPa.m1/2

Answer 1

1.5510 mm

Step-by-step explanation:

Plane strain fracture toughness = 45 MPa√m

failing stress ( б ) = 300 MPa

maximum length of surface crack ( a )= 0.95 mm

Determine maximum allowable surface crack length ( in mm )

we will make use of this relationship for Design stress equation to determine the value of Y

б =
`(k)/(y√(\pi *a) )` --------- ( 1 )

k = 45 MPa√m

б = 300 MPa

a = 0.95 mm

y = ?

From equation 1 make Y subject of the equation ( also substitute values into equation 1 above )

hence ; y = 2.7457

Now determine maximum allowable surface crack when component is exposed to a stress of 300 MPa and made from another alloy with plane-strain fracture toughness of 57.5 MPa√m

we will apply the equation

б =
`(k)/(y√(\pi *a) )` --------- ( 2 )

K = 57.5 MPa√m

б = 300 MPa

y = 2.7457

a ( maximum allowable surface crack ) = ?

from equation make a subject of the equation

a =
`(1)/(\pi ) ((k)/(\alpha y) )^(2)`

a =
`(1)/(\pi ) ((57.5)/(300*2.7457) )^2` = 1.5510 mm