Question

An aircraft component is fabricated from an aluminum alloy that has a plane strain fracture toughness of 37 MPam. It has been determined that fracture results at a stress of 206 MPa when the maximum (or critical) internal crack length is 2.58 mm. a) Determine the value of Yσπa for this same component and alloy at a stress level of 267 MPa when the maximum internal crack length is 1.29 mm.

Answer 1

we are supposed to determine the stress level at which a wing component on an aircraft will fracture for a given toughness of
`37 MPa√(m)` and maximum internal crack length
`1.29 mm` , given that fracture

occurs for the same component using the same alloy at one stress level
`206 Mpa` and another internal crack length (2.58 mm). It first becomes necessary to solve for the parameter Y for the conditions under which fracture occurred , therefore

`Y=(K_(lc) )/(sigma√(\pi a ) )`

`=(37Mpa√(m) )/(206Mpa)\sqrt{\pi (2.58*10^-^3m)/(2) } \\=2.82`

`sigma_(c) =K_(lc) /Y√(\pi a )`

`=(37MPa√(m) )/(2.82)\sqrt{\pi (1.29*10^-^3)/(2) } \\= 293 MPa`