An aircraft component is fabricated from an aluminum alloy that has a plane strain fracture toughness of 30 . It has been determined that fracture results at a stress of 237 MPa when the maximum (or critical) internal crack length is 2.78 mm. a) Determine the value of for this same component and alloy at a stress level of 355 MPa when the maximum internal crack length is 1.39 mm.

Answer:

fracture will occur since ( 31.8 Mpa√m ) is greater than the [tex]K_{Ic[/tex] of the material ( 30 Mpa√m )

Explanation:

Given the data in the question;

To determine whether the aircraft component will fracture, given a fracture toughness of 30 Mpa√m, stress level of 355 and maximum internal crack length of 1.39 mm.

On a similar component, it has been said that fracture results at a stress of 237 MPa when the maximum (or critical) internal crack length is 2.78 mm.

so we first of all solve for the parameter Y in the condition where fracture occurred.

[tex]K_{Ic[/tex] = 30 Mpa√m

σ = 237 MPa

2α = 2.78 mm = 2.78 × 10⁻³ m  

so

Y = [tex]K_{Ic[/tex] / σ√πα

we substitute

Y = (30 Mpa√m) / (237 MPa)√(π(2.78 × 10⁻³ m / 2 ) )

Y =  (30 Mpa) / (237)( 0.06608187 )

Y = 30 / 15.6614

Y = 1.9155

Next we solve for Yσ√πα for the second case;

σ = 355 Mpa, 2α = 1.39 mm = 1.39 × 10⁻³ m

so

Yσ√πα = 1.9155 × 355 Mpa × √( π × (1.39 × 10⁻³ m / 2) )

= 1.9155 × 355 × 0.0467269

= 31.8 Mpa√m

so

( 31.8 Mpa√m ) > [tex]K_{Ic[/tex] ( 30 Mpa√m )

Therefore, fracture will occur since ( 31.8 Mpa√m ) is greater than the [tex]K_{Ic[/tex] of the material ( 30 Mpa√m )

The 150 mm thick wall of a gas fired furnace is constructed of fireclay brick (k=1.5 W/m.K) , tho=2600 kg/m3, and cp=1000 J/kg.K ) and is well insulated at its outer surface. The wall is at a uniform initial temperature of 20 degree C, when the burners are fired and inner surface is exposed to products of combustion for which T infinity=950 degree C and h=100 W/ m2.K.
(A) How long does it take for the outer surface of the wall to reach a temperature of 750 degree C?
(B) plot the temperature distribution in the wall at the foregoing time.

A fuel oil is burned with air in a furnace. The combustion produces 813 kW of thermal energy, of which 65% is transferred as heat to boiler tubes that pass through the furnace. The combustion products pass from the furnace to a stack at 6500C. Water enters the boiler tubes as a liquid at 200C and leaves the tubes as saturated steam at 20 bar absolute. Calculate the rate (kg/h) at which steam is produced.

A piece of corroded steel plate was found in a submerged ocean vessel. It was estimated that the original area of the plate was 5 in.2 and that approximately 2.3 kg had corroded away during the submersion. Assuming a corrosion penetration rate of 200 mpy for this alloy in seawater, estimate the time of submersion in years. The density of steel is 7.9 g/cm3.

The atomic weights of C and H are 12 and 1, respectively. The chemical formula of polyethylene is (C2H4)n. The number average mean molecular weight of polyethylene with a degree of polymerization of 12,000 is:_____.
a. 120,000.
b. 336,000.
c. 280,000.
d. 296,000.