Question

An aircraft component is fabricated from an aluminum alloy that has a plane strain fracture toughness of 39 . It has been determined that fracture results at a stress of 208 MPa when the maximum (or critical) internal crack length is 2.82 mm. a) Determine the value of for this same component and alloy at a stress level of 270 MPa when the maximum internal crack length is 1.41 mm.

Answer 1

`27.57713\ MPa√(m)`

Step-by-step explanation:

Y = Fracture parameter

a = Crack length

`\sigma` = Stress in part

Plane strain fracture toughness is given by

`K_I=Y\sigma√(\pi a)\\\Rightarrow Y=(K_I)/(\sigma√(\pi a))\\\Rightarrow Y=(39)/(270* √(\pi 0.00282))\\\Rightarrow Y=1.53462`

When a = 1.41 mm

`K_I=Y\sigma√(\pi a)\\\Rightarrow K_i=1.53462* 270√(\pi 0.00141)\\\Rightarrow K_I=27.57713\ MPa√(m)`

The value of plane strain fracture toughness is
`27.57713\ MPa√(m)`