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

1.5510 mm

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 =    --------- ( 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 =    --------- ( 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 =  

a =  =   1.5510 mm

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