An aircraft component is fabricated from an aluminum alloy that has a plane strain fracture toughness of 32 . It has been determined that fracture results at a stress of 219 MPa when the maximum (or critical) internal crack length is 2.68 mm. a) Determine the value of for this same component and alloy at a stress level of 284 MPa when the maximum internal crack length is 1.34 mm.

Respuesta :

[tex]\frac{32}{219x0.006488}[/tex]Answer:

The answer is 309MPa

Explanation:

It first become necessary to solve for the parameter Y for the conditions under which the fracture occurred using below equation

Y = δ[tex]\frac{kic}{δ\sqrt{\pia} }[/tex][tex]\pi a[/tex]  

= [tex]\frac{32}{219\sqrt{\pi }\frac{2.68x10^-3}{2} }[/tex]

=[tex]\frac{32}{219\sqrt{0.00421} }[/tex]

= [tex]\frac{32}{219*0.06488}[/tex]

[tex]\frac{32}{14.2097} =2.25[/tex]

[tex]\frac{Kic}{y\sqrt{\pia } }[/tex][tex]\pi[/tex]a   = [tex]\frac{32}{2.25\sqrt{\pi \frac{1.34*10^-3}{2} } }[/tex]

[tex]\frac{32}{2.25\sqrt{\pi*0.00067 } }[/tex]

=[tex]\frac{32}{2.25\sqrt{0.00211} }[/tex]

= [tex]\frac{32}{2.25 * 0.0459}[/tex]     = [tex]\frac{32}{0.1034}[/tex]

= 309MPa