K_(IC)=Y_(sigma )sqrt (pi a) (c) Some aircraft component is fabricated from an aluminum alloy that has a K_(IC) of 35 MPa m^1/2 , it has been found that fracture occurs at a stress of 250 MPa when the critical (maximum) crack length is 2.0 mm. For the same aircraft component will fracture occur at a stress level of 325 MP when the crack length is 1.5 mm ? Why or why not?

To determine whether the aircraft component will fracture at a stress level of 325 MPa when the crack length is 1.5 mm, we need to compare the stress intensity factors at the two different crack lengths.<br /><br />The stress intensity factor (K_IC) is a measure of the stress concentration around a crack in a material. It is defined as the stress at a distance from the crack tip that is proportional to the square root of the crack length (a).<br /><br />In this case, the aluminum alloy has a K_IC of 35 MPa m^1/2. This means that the stress at a distance from the crack tip that is proportional to the square root of the crack length (a) is 35 MPa m^1/2.<br /><br />When the crack length is 2.0 mm, the stress intensity factor is 35 MPa m^1/2. When the stress level is 250 MPa, the stress intensity factor is 250 MPa.<br /><br />To determine whether the component will fracture at a stress level of 325 MPa when the crack length is 1.5 mm, we need to calculate the stress intensity factor at this crack length and compare it to the stress level of 325 MPa.<br /><br />The stress intensity factor at a crack length of 1.5 mm can be calculated using the formula:<br /><br />K_IC = Yσ√(πa)<br /><br />where Y is a dimensionless factor that depends on the geometry of the crack and the material, σ is the stress, and a is the crack length.<br /><br />Assuming that the same material and geometry are used, we can calculate the stress intensity factor at a crack length of 1.5 mm as:<br /><br />K_IC = Yσ√(πa)<br /><br />K_IC = Y(325 MPa)√(π(1.5 mm))<br /><br />K_IC = 325 MPa√(π(1.5 mm))<br /><br />K_IC = 325 MPa√(4.54)<br /><br />K_IC = 325 MPa(2.14)<br /><br />K_IC = 700 MPa m^1/2<br /><br />Since the stress intensity factor at a crack length of 1.5 mm (700 MPa m^1/2) is greater than the stress level of 325 MPa, the component will fracture at this stress level.<br /><br />Therefore, the answer is yes, the aircraft component will fracture at a stress level of 325 MPa when the crack length is 1.5 mm.