**Materials Science and Engineering Assignment 06**

1. It is known that the yield strength of an iron is related to grain diameter as shown in the table. Determine the grain diameter that would have yield strength of 205 MPa.

Grain Diameter (mm) Yield Strength (MPa)

5 x 102 135

8 x 103 260

= Using Hall Petch relationship, 205 Mpa would have grain diameter of 6 x 10-3 mm

2. (a) What is the approximate ductility (%EL) of a brass that has yield strength of 275 MPa?

(b) What is the approximate Brinell hardness of 1040 steel having yield strength of 690 MPa? Hint: refer to Figure 7.19 in the textbook.

3. (a) What is the maximum tensile load P that can be applied without causing yielding of the material?

(b) Indicate in the drawing where you expect cracks to initiate and the direction of crack propagation if an excessive load is applied. Yield strength of the material is 475 MPa.

4. While inspecting a machine using x-ray, you found an internal crack of length 4 mm perpendicular to a stress in service. If the material has a plane-strain fracture toughness of 28 MPa m , what is the limiting stress for a factor of safety of 1.5?

5. A 12.5-mm-diameter cylindrical rod of 2014-T6 aluminum alloy is subjected to a repeated tension-compression load cycling along its axis. Computer the maximum and minimum loads (force) that can be applied to have a fatigue life of at least 1.0 x 107 cycles. Assume a mean stress of 50 MPa. Hint: reference page 32 of lecture file 140305.

6. A flat plate is subjected to constant-amplitude uniaxial cyclic tensile and compressive stresses of 120 and 35 MPa, respectively. If the largest initial surface crack is 1.00 mm and the material has a plain-strain fracture toughness of 35 MPa m , estimate the fatigue life.

7. A flat plate is subjected to constant-amplitude uniaxial cyclic tensile and compressive stresses of 120 and 35 MPa, respectively. Compute the critical internal crack length if the fatigue life must be a minimum of 0.7 x 106 cycles. The maximum initial internal crack length is 0.8 mm. The Paris equation for the material is da/dN = (7.5 x 1013)(K)1.8 in MPa and m units. The geometric correction factor is 1.12.